Inside Matthew Broderick and Mel Brooks' Unofficial 'Producers' Reunion on 'Only Murders'

Executive producer Jess Rosenthal exclusively tells PEOPLE how the two guest stars found their way into the newest episode of the Hulu series

Tuesday's Only Murders in the Building was a happy reunion for Broadway fans as it reteamed Matthew Broderick and Mel Brooks once again two decades after their film and stage triumphs with The Producers.

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In this week's episode, as Broderick played an outlandish version of himself poised to potentially replace Charles (Steve Martin) in Oliver's (Martin Short) upcoming musical, Brooks popped in for a brief cameo via FaceTime to hilariously trash-talk Broderick.

One would imagine that casting two screen and stage legends might have been a difficult feat, but OMITB executive producer Jess Rosenthal tells PEOPLE getting Broderick, 61, and Brooks, 97, to sign on was surprisingly easy.

In fact, Broderick — who played The Producers' hapless accountant Leo Bloom — was more than game to play an "out-of-control" caricature for the Hulu series.

"One is never sure how an actor might react to playing a version of himself," Rosenthal says. "Will they be skittish about going too far? Are there aspects of their life they won't wish to pick at? Happily, Matthew was just the opposite. He found it all hysterical and kept asking to push it further and further."

Broderick's eccentric on-screen antics, which included an insane level of perfectionism, were actually improvised by the performer.

"Matthew brought this wonderful tone to it all," says Rosenthal, who assures that Broderick is actually very "warm and collaborative" in real life. "I love that his incredible devotion to acting and authenticity becomes the very thing that causes Oliver so much grief."

Soon after realizing Broderick was difficult to deal with, Oliver FaceTimed Brooks, who warned him not to cast the performer in his musical. But when Oliver confessed it was too late, the comic legend responded, "Oh, Oliver, you're f---ed."

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It was also a reunion for Short, 73, who played Leo Bloom in the 2003 Los Angeles production of The Producers two years after the historic Tony-winning success of Brooks' Broadway adaptation of his 1967 silver screen comedy. (In the West Coast production, Seinfeld alum Jason Alexander stepped into the co-lead role of Max Bialystock, which Nathan Lane originated on the Great White Way.)

Despite this triple reunion being long in the making, it actually came together extremely quickly when it came to Brooks' cameo. The Blazing Saddles director opted in just days before production started on episode 7 in a moment that elicited excitement from the crew.

"We dreamed of the great Mel Brooks, and [were] overjoyed that our wish came true," says Rosenthal, recalling the moment the crew heard the news Brooks had agreed to shoot his scene. "'Did you hear, did you hear? He's doing it!"

Related: Mel Brooks' Life in Photos

While his scene runs just 38 seconds, accomplishing it took some technical ingenuity behind the scenes. The crew had "multiple" meetings to prepare for little details, including what communications device they should they use, how the actors would see one another, what the crew's cameras would capture and how the actors' eyelines would match up.

"We imagined complications at every turn, but in practice it became quite simple," Rosenthal explains. "Two all-time legends and pros in Mel and Marty got on, shared a laugh at their history together ... ran the scene twice, and after five minutes we had it." 

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Only in the Building airs on Tuesdays on Hulu.

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