The Holy Grail, Everest, the fifth star, whatever they call it, Leinster have failed to find what was needed to get their hands on the Champions Cup for the last five years.
And boy, have they tried.
A "sick obsession" was what James Lowe called their mission to conquer Europe for the first time since 2018.
Today, the two titans of European rugby, Leinster and Toulouse, meet for the 15th time.
Their duels go back to a first clash in 1997, but incredibly, despite nine tournament wins between them, they have never faced off in a final.
This star war has the star power and it promises to be a battle for the ages.
The linchpins of the France national side, among them Antoine Dupont and Romain Ntamack, take on the cream of the crop of the Ireland team, Jamison Gibson-Park and Caelan Doris to name just two, and if the last three Tests between the nations are any indication of what's to come, a real treat lies in store.
Incidentally, Ireland won two of the last three of those games and they’ve been ferocious, high-quality affairs all.
They stood in contrast to how Leinster won their semi-finals over Toulouse in the last two years.
Despite their European pedigree, the Toulouse teams that turned up for the 40-17 and 41-22 defeats in Dublin did not display the heart for the fight they normally do.
Leinster, meanwhile, were ruthless in both those outings, keeping their foot on the Toulouse throat until ill-discipline and disinterest set in.
Leo Cullen and his side can only take so much from those games and the Tottenham Hotspur Stadium, expecting a full house of 62,850 today, won’t be a daunting location for the French visitors.
They have hit a magical run of form, too, leading the Top14 with four wins in their last five, in addition to, at times, mesmerising victories over Harlequins (38-26) and Exeter (64-26) in the semi and quarter-finals, respectively.
Meanwhile, Leinster’s run to the final should stand to them in a different way.
The crushing of nemesis La Rochelle (40-13) in the quarter-final is a blueprint they can work off, reflected in today's matchday squad; the nervy win over Northampton (20-17) will focus the mind, demonstrating how delicate perceived dominance can be against a top-class opposition.
Their defeat to Ulster last weekend, "a shot across the bow", said assistant coach Robin McBryde, another reminder of the importance of taking the right decisions at the right time.
There are numerous intriguing individual battles in store.
Two of the form players in the world right now face off.
Dupont, looking fresher than ever after his sojourn with the Sevens, taking on Gibson-Park (below), who has raised his game to a new level again this season, starring for Ireland in the Six Nations and unplayable in the knock-out phase of this competition.
His display and 17-minute hat-trick against Leicester Tigers in the last-16 was up there with the best performances on the island in years and his speed of thought set up James Lowe for his first two tries against Saints.
"These are the moments you dream of in my position, he’s the best player in the world these last few seasons," said the New Zealand native of his direct opponent.
"It’s a huge challenge for players in our position. But it’s the team who are facing him."
At out-half, Ross Byrne is a steady hand but comes up against the mercurial Ntamack, back from long-term injury and capable of winning a match in an instant with a perfect pass or turn of foot from anywhere on the field.
The fit-again Hugo Keenan is a major threat for Leinster, who lacked cutting edge from the backfield in his absence, while Blair Kinghorn keeps Thomas Ramos out of the Toulouse line-up.
"When you're lucky enough to have such players at your disposal, naming your starting team is a real puzzle," boss Ugo Mola, who named an unchanged side from their semi-final, said.
Joshua Brennan, son of former Leinster, Toulouse and Ireland forward Trevor, is on the bench.
The midfield make-up is similar on both sides. Robbie Henshaw has taken Jamie Osborne under his care and the young inside centre has blossomed. So too the experience of Pita Ahki has allowed U20s star Paul Costes to shine.
Tadhg Furlong will lock horns with Cyril Baille to set the tone for the scrum battle, while Joe McCarthy, man of the match when Ireland beat France in Marseille just over three months ago, can again show his mettle, this time against the giant Emmanuel Meafou and Thibaud Flament.
Cullen has again opted to start Will Connors, who is once more being used as a bespoke chop-tackling weapon to deal with the French ball-carriers.
He started both wins over the reigning champions but missed out completely in the semi-final victory. There is once again a 6:2 bench split; Ciarán Frawley is preferred over Jimmy O'Brien, while Josh van der Flier and James Ryan are to play their parts off the bench.
Garry Ringrose's shoulder issue keeps him out of contention.
Physically the teams are very evenly matches but the game is about the top two inches. If managers didn’t believe that then they wouldn’t employ performance coaches, much heralded by the players in dispatches.
How heavily will Leinster’s failure to get over the line in three finals since their 2018 victory weigh on the collective mind? The point was made during the week that they didn't just lose to La Rochelle in Dublin, they blew it.
There is some new blood but nine of the matchday 23 that lost to Saracens in the final of 2019 are among the squad today and the majority have been present for the heartache of decider losses in 2022 and even more jarringly, last season’s defeat.
It was all set up for Leinster but they couldn’t close the deal, even with a 23-7 advantage.
That they are within sight of the mountain top again is itself a testimony to their fortitude.
There is, of course, the not-insignificant addition of one Jacques Nienaber (below) to the Leinster coaching ticket.
The ex-Springboks boss, who in conjunction with Rassie Erasmus, oversaw two World Cup wins and anyone who saw the fly-on-the-wall Chasing the Sun 2 documentary knows exactly the kind of performances Nienaber elicits from his charges.
"We’ve done our best in the last two finals, but this season we’ve put everything in trying to move forward with the arrival of some new coaches, who have changed a lot of things," Gibson-Park added.
"Jacques has a great personality and gives off positive energy to the squad.
"We hope that our defensive system will make the difference in the final by disrupting a Toulouse team who like to run with the ball a lot.
"It’s going to be a magnificent battle."
LEINSTER v TOULOUSE: ALL YOU NEED TO KNOW
The tale of the tape gives Toulouse, last winners in 2021, an advantage.
While Leinster have been learning off Nienaber’s new creed, with linespeed and suffocation to the fore, the Top14 side have been busy topping the charts for points (311), tries (46), carries (896), metres made (3,716), clean breaks (97), and defenders beaten (167).
Leinster, who topped Pool 4 with wins over La Rochelle, Stade, Sale and Tigers, feature at the top of the passes count with 1,088.
The stage is set - Leinster and Toulouse ready for Champions Cup final showdown #RTERugby #RTESport #LEIvTOU
— RTÉ Sport (@RTEsport) May 25, 2024
Live on @RTE2 @RTEplayer @RTERadio1 kick-off 2.45pm pic.twitter.com/kZfohEaVWk
Three of the Toulouse team pack the offload charts: Dupont with 20, Meafou with 16 and Ahki with 12. Danger everywhere.
Defeat this afternoon for the Irish side would mean a record fourth final loss, eclipsing Leicester, Clermont and Racing’s unwanted hat-trick.
As for Toulouse, including Europe and the Mad Max race that is the Bouclier de Brennus, the club is contesting a 38th final; they have won 27.
Previous meetings between the sides have tended to be one-sided but it seems almost impossible to split the teams today.
Leinster must also manage Matthew Carley; crucial to winning the scrum and breakdown battle is getting on the English referee's good side early.
One title in 12 years would be a pitiful return for the quality that Leinster have, their hurt locker is full at this point.
They must reach the heights they managed against La Rochelle in order to prevail.
Verdict: Leinster
Leinster: Hugo Keenan; Jordan Larmour, Robbie Henshaw, Jamie Osborne, James Lowe; Ross Byrne, Jamison Gibson-Park; Andrew Porter, Dan Sheehan, Tadhg Furlong; Joe McCarthy, Jason Jenkins; Ryan Baird, Will Connors, Caelan Doris (capt).
Replacements: Rónan Kelleher, Cian Healy, Michael Ala'alatoa, James Ryan, Jack Conan, Luke McGrath, Ciarán Frawley, Josh van der Flier.
Toulouse: Blair Kinghorn; Juan Cruz Mallia, Paul Costes, Pita Ahki, Matthis Lebel; Romain Ntamack, Antoine Dupont (capt); Cyril Baille, Peato Mauvaka, Dorian Aldegheri; Thibaud Flament, Emmanuel Meafou; Jack Willis, Francois Cros, Alexandre Roumat.
Replacements: Julien Marchand, Rodrigue Neti, Joel Merkler, Richie Arnold, Joshua Brennan, Paul Graou, Santiago Chocobares, Thomas Ramos.
Referee: Matthew Carley (RFU)
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