Nicolas Cage Shares Meaningful Oscars Moment He Had with Bradley Cooper: 'I Admire' Him (Exclusive)

Nicolas Cage is a big fan of Bradley Cooper and his craftsmanship.

The Oscar-winning actor, 60, attended the South by Southwest premiere of his new film Arcadian on Monday in Austin, Texas, just one day after attending the 2024 Oscars on Sunday night in Los Angeles.

On the red carpet, Cage told PEOPLE one filmmaker he'd still like to work with after a long Hollywood career is Cooper, 49.

"I think Bradley Cooper is a hell of an actor. I admire what he's accomplished," says Cage. "Jerry Lewis used to tell me, 'You're not a filmmaker unless you star in your own movie and direct your own movie, and compose and edit your own movie.' And Bradley's doing that."

Cage added of a moment he had with Cooper at the Oscars, "I told him last night ... and I am very impressed with that."

Cooper, who made his directorial debut with 2018's A Star Is Born, landed several Oscar nominations this year for Maestro, the Leonard Bernstein biopic that he co-wrote, directed and starred in.

Cage, who won his Oscar in 1996 for Leaving Las Vegas, was a presenter at this year's ceremony, selected to introduce the "brilliant" Paul Giamatti onstage during the Best Actor portion of the night. (Cillian Murphy went on to win the category for Oppenheimer.)

Matthew McConaughey, who picked up his win in 2014 for Dallas Buyers Club, paid tribute to Cooper onstage.

"A modern-day renaissance man. Nothing better describes you, sir, Mr. Bradley Cooper," said McConaughey, 54, pointing to the star in the audience, "who wrote, directed, produced and acted in his latest film, Maestro."

"From the script to the screen," he continued, "Bradley takes a transformative journey into becoming Leonard Bernstein, bringing to life all the character, charisma and complex brilliance of an American icon. Congratulations, Bradley."

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Two of Cage's young costars from Arcadian told PEOPLE at SXSW on Monday about working with the longtime actor on the project.

"He brought this calmness to the set, which I think is probably necessary for someone like him," says Jaeden Martell, 21. "I think he's 'Nicolas Cage' and everyone gets excited to be around him, and he has this energy that calms people and makes them feel comfortable."

Maxwell Jenkins, 18, adds that Cage "was so collaborative on the project. Getting to come and learn from the master — but a master who was willing to listen and work on the scenes with you — I really appreciated."