NEW YORK – Josh Gad and Andrew Rannells can switch characters at the drop of a hat. Quite literally, in fact.

In “Gutenberg! The Musical!”, the actors play dozens of roles in 105 minutes, all clearly marked by bold-lettered baseball caps that they alternate between. The zany Broadway comedy follows theater writers Bud (Gad) and Doug (Rannells) as they earnestly pitch a musical about Johannes Gutenberg, inventor of the printing press. They perform the ludicrous new show in its entirety for prospective producers (or rather, the audience at New York's James Earl Jones Theatre).

It wasn’t until the first reading of “Gutenberg!,” which officially opens Thursday, that Gad had any idea about the show’s hamster wheel of headwear.

“I almost had a heart attack,” he recalls, in a joint interview with Rannells. “We only had a three-week rehearsal process, so it was beyond nerve-racking. It’s definitely a mathematical equation of comedy.”

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“Gutenberg!” marks the first time that Rannells, 45, and Gad, 42, have been onstage together since 2011’s “The Book of Mormon,” the irreverent satire that won nine Tony Awards including best musical. Their latest outing is already proving to be another box-office hit, thanks to their draw as a comedic duo.

“They’re both wildly inventive comedians,” says Alex Timbers, the show’s director. “It isn’t so much that one person’s always the straight man – they just have an amazing dynamic where they know how to play off each other in such an extraordinary way.”

The actors tell us more about “Gutenberg!,” worst jobs and their “Mormon” celebrity run-ins:

Question: As absurd as “Gutenberg” gets, it’s ultimately very sweet and even emotional. Was that surprising?

Andrew Rannells: We knew it was very silly and this great love letter to musical theater. But as we read it, the heart (became evident). There’s no snarkiness or cynicism to it. These are two guys who very much love each other and have this common goal. It’s really rare to find – especially a comedy script these days – that has that sort of core. So that was a big part (of the appeal) for me, especially to do it with a very good friend. Josh and I now bring 10-plus years of friendship to this show, and that’s a pretty unique experience to have the material sort of mirror our actual friendship.

Bud and Doug work at a nursing home to make ends meet. What’s the most memorable job you had before acting took off?

Josh Gad: A friend of our family hired me to work at an ad firm. There was a company called 1-800-Telemattress and he asked me to pitch a campaign. I was like, “OK, I’m going to come up with something great.” So I walked into his office and go, “Are you feeling tired? Tell a mattress!” And he goes, “Josh, I don’t think this is the right path for you.”

Rannells: I was a greeter at the Warner Bros. Store. I had to wear a Looney Tunes letterman jacket, and stand there and say, “Welcome to the Warner Bros. Store. Eight floors of fun!” I had to say that like 500 times a day. The day that I quit, this woman came up to me and said, “Where are the Tweety Bird mud flaps?” And I was like, “I can’t do this anymore. I know I have bills to pay, but I just can’t.”

What about a worst audition story?

Gad: I was auditioning to get into Juilliard. Michael Kahn, who ran the program at the time, was sitting there with what looked like the group of bad guys from “Superman 2.” They were all sitting there staring me down, black hair slicked back, looking like they were ready to kill Superman. I was so intimidated and forgot the entire monologue. I then started improvising in iambic pentameter and it was an absolute disaster. I go, “I will show myself out now. Thank you all very much.”

Rannells: It was for the revival of “South Pacific” at Lincoln Center. I was on this kick at the time of singing the same song for every audition and just letting the chips lay. I was like, “Whatever! If they like it, they like it.” So I went in for (director) Bartlett Sher and sang “Born to Run” by Bruce Springsteen. He looked at me and went, “Well, you’re very talented. But not for this show.”

Looking back, was there a moment when you realized “The Book of Mormon” was a hit?

Gad: I was convinced “Mormon” was going to run for three months and close. People forget that we were being written off before we even opened: “It’s too controversial! You’re going to have picketers! It’ll be a disaster!” And then the fifth or six (performance), I remember seeing a line of 150 people outside the theater waiting for lottery tickets. Then the next day, it ballooned to 400. I remember looking at Andrew and going, “This feels like something very big.” And then it just exploded from there.

Rannells: There was a night maybe a month into the show when Will Ferrell came with his wife and they were so nice. And then he was like, “Do you guys want to come to dinner?” Josh and I were like, “Uh, yeah! OK!” So we went to dinner at Orso on 46th Street. Martin Short came in, and it just felt like a piece of New York that I knew existed but had never been a part of before.

Gad: You always hear that expression “the toast of the town,” but when you actually become “the toast of the town,” it’s a very surreal experience. Tom Hanks is coming to your show one night, Bono’s there the next night, and they want to meet you!

Rannells: And the whole cast was old enough to know it was a moment. We were extremely grateful for the opportunity, we knew it wasn’t going to last forever, and we just jumped on it. We went to the dinners and the parties, because we knew this was only going to happen for a little while.

Gad: Now we’re both in our 40s and we just want to go home after every show.

So do you have a favorite celebrity who came to “Mormon?”

Rannells: It was often the “Sophie’s choice” of celebrities: “Who do you talk to first?” There was one night where it was Bernadette Peters and Sean Penn, and I just beelined to Bernadette. I was talking to her for a while and she was like, “Don’t you want to go talk to Sean Penn?” And I said, “Honestly, no.” I was like, “My little childhood brain would be exploding right now if it knew that in many years, I would actually be hugging and talking to Bernadette Peters.”

Gad: By the way – that means I got stuck with Sean Penn.