You’ve been on “The Daily Show” since 2014, but you became much more visible after hosting the White House correspondents’ dinner earlier this year. In that performance, you said that nobody else wanted this gig — why was that? It just became this hot potato that nobody wanted to touch. When I got the call, I was like: “We’re 19 days away. No one wanted this part.” Larry Wilmore did it last year, and they asked him four and a half months before the announcement came out. When I called Larry to tell him, he said, “They just called you?”

Be honest: How mad were you when Jon Stewart left the show so soon after hiring you? I was looking at how much rent was in New York, so I told him, “I just signed a lease!” But he’s such a calm, sage guy — he told me and the other new correspondents that everything was going to be all right, and he believed in us.

You were asked to not really roast the president during the W.H.C.D., but you obviously went after him a little bit. Was there someone who gave you the go-ahead, or did you just have to trust your own gut? I trusted my gut. I always knew that if I was cutting, but not cruel, I would be in the right. I don’t ridicule someone’s merit, or something that they can’t control. If I were to say, “Steve Bannon looks like a bunch of chicken cutlets stapled together” at a comedy club, everyone would be roaring, but to me, I’m like, How would I feel if someone was like, “Hasan Minhaj looks like a poop stain?”