The Emmy-winning Veep star, 50, plays twin brothers Mr. Benedict and Mr. Curtain in the Disney+ series The Mysterious Benedict Society (June 25). The whimsical story unfolds as Benedict recruits orphans to go undercover for a secret mission at Curtain’s boarding school.

What’s the appeal of The Mysterious Benedict Society? There’s something called the Emergency in the book [on which the series is based] that’s creating all this panic and anxiety. We were in production in the middle of the pandemic, and this just seemed to parallel what was happening, and so I was really drawn to it.

Tell us a little bit more about your characters. Benedict is this kind of mad scientist—erratic, kind, affable and nutty professor-ish. His brother, Curtain, is just the opposite, incredibly manipulative and cunning. It was fun to play those opposites.

You’re always going to be known for Veep. What was that experience like? This sounds cheesy, but it’s true: It’s the relationships. We got very close. We still hang out. I never really watched the episodes, but I always watched the gag reels, because that’s what I remember—the times that we were cracking up, chatting and hanging out.

You play writer-producer Jess Oppenheimer in Amazon Studios’ upcoming Being the Ricardos, about a week behind the scenes at the TV series I Love Lucy. Were you a Lucy fan? I grew up watching I Love Lucy. She was such an amazing physical comedian. [The series is about] a lot of stuff that happens within that one week. You find out about Desi and Lucy’s relationship. Aaron Sorkin’s directing it, and Javier Bardem is playing Desi Arnaz and Nicole Kidman is Lucille Ball.

What advice did he get from Veep’s Julia Louis-Dreyfus? Go to Parade.com/hale to find out.