At first, it appears we’re going to get a new Bill Burr in Drop Dead Years, a kinder, gentler comedian to lead us through the dark times. In Burr’s new Hulu special that drops today, he delivers an earnest confession before he even takes the stage, a voice-over soliloquy born of years in therapy: “I thought I did stand-up because I loved comedy. Then what I really figured out is, no, that’s not why I did it,” he explains, leaning against an old brick building in some urban dreamscape. “I did stand-up because that was the easiest way to walk into a room full of a bunch of people that I didn’t know and make everybody like me.”

Whoa — that’s deep, Bill. And he’s just getting started as he makes his way from the shadows to the stage. “The way I’ve moved through...