The 60-year-old actor hit the stage at the Santa Barbara International Film Festival Thursday to give his 49-year-old compadre the Outstanding Performer of the Year Award for his part as Leonard Bernstein in "Maestro" -- a movie he also directed and co-wrote.

It's a top honor at the event ... and it gave BP the opportunity to talk about Cooper's work through the years -- including the moment he knew BC was gonna be big.

"Maestro" is the fifth performance for which Cooper received an acting Academy Award nod BTW ... but Pitt didn't point to any of those performances -- instead he heaped praise on Cooper for his role in "The Hangover."

Pitt pointed out the subtle intricacies of Cooper's performance -- saying so many of the moments Cooper makes great have very little to do with him ... improving the film from the side of the screen in a sense. Pretty impressive for a movie where one of the main characters is a tiger!

The Oscar-winner didn't just talk about "The Hangover" though ... he also brought up Cooper's "A Star is Born" performance and direction -- noting Cooper somehow balanced emotional drunk acting scenes while also keeping an eye on the crew to make sure he's getting the perfect shot.

Brad added, "To do that really, really well is nothing short of perfect."

Hopefully, the Academy feels the same way ... Cooper's up for Best Actor for his role in the movie at this year's Oscars -- an award he's 0-for-3 on so far.