Mel Brooks’s human comedy gets a ‘Part II’ for streaming TV, with a sketch-star cast and a sharp makeover.Before his many lives as America’s tummler-in-chief — movie star, director, Broadway producer — Mel Brooks was a TV guy. He wrote for Sid Caesar’s “Your Show of Shows,” the Big Bang from which much of the TV comedic tradition exploded forth. His 1981 film, “History of the World, Part I” (in which Caesar appeared as a cave dweller), applied an episodic approach, as if it were meant to be a sketch-comedy series.Now, with a little help and a few changes, it is. The eight-part “History of the World, Part II,” which debuts two episodes a day from Monday through Thursday on Hulu, is a screwball tour of civilization that gives the Brooks formula enough contemporary updates that you could think of it as “Evolution of TV Comedy, Part I.”And in an era of dutiful brand extensions and pointless revivals, it turns out to be history that’s surprisingly worth repeating.The 96-year-old Brooks is a writer and producer of the new series and assumes the narrator role performed by Orson Welles in the film. He has limited screen time now — the heaviest lifting is done by the writer-producer-performers Ike Barinholtz, Nick Kroll and Wanda Sykes — but he is responsible for the show’s first sight gag, in which he’s digitally altered into a young, musclebound hunk.Like that image, “Part II” aims not simply to reproduce the Mel Brooks of the last century but also to bring his comedy into 2023. It’s a collaborative production (the cast is so vast it might be easier to list TV-comedy fixtures who don’t appear) that is more diverse in both faces and comedy styles. Beyond the callbacks to the movie and affectionate recreations of Brooks’s slapstick and Jewish humor, the series combines elements of “Kroll Show,” “Drunk History,” “Documentary Now!,” “Sherman’s Showcase” and more.“Part I” was less a parody of actual history than of movie history. Its ancient Rome was lifted from swords-and-sandals epics; its French Revolution was, as the New York Times critic Vincent Canby wrote, very much the one imagined in M.G.M.’s “A Tale of Two Cities.”“Part II” is thoroughly made of TV and pop-media references. The story of Jesus Christ begins with a dead-on parody of “Curb Your Enthusiasm,” with Kroll as a Larry Davidian Judas riffing with J.B. Smoove as the apostle Luke; later it becomes a drawn-out sendup of the Beatles documentary “Get Back.”“Part II” is hit-and-miss, much like “Part I” and nearly every sketch comedy ever made. When it hits, it’s an almost perfect marriage of style and subject. The strongest extended sketch stars Sykes as Shirley Chisholm — the Black female congresswoman and 1972 presidential candidate — in a note-perfect sendup of a ’70s sitcom. It’s not just impeccably executed and detailed, it’s sharp, smart history, accented with the laughter of a “live Black audience.”When the show misses — well, another advantage streaming has over the movie theater is the fast-forward button. A running bit about Gen. Ulysses S. Grant (Barinholtz) trying to kick his booze habit starts off strong with Timothy Simons as a cranky Abraham Lincoln but becomes a grinding war of attrition. The limp gag of imagining historical figures on social media (Galileo, Typhoid Mary, Princess Anastasia) doesn’t improve with repetition.The many guest stars include, from left, Rob Riggle, Richard Kind and Zazie Beetz.Aaron Epstein/HuluThere’s also the occasional reminder of the changed cultural sensibilities that “Part II” was made for. Brooks was a yukmeister provocateur, who made fun of the horrors of the 20th century (and beyond) while trusting his audience to get the absurdity. His “The Producers” — about the making of a deliberately offensive musical about Hitler — was about that kind of trust backfiring, and it generated backlash in real life.But as Brooks said on “Fresh Air” last year, “If we’re going to get even with Hitler, we can’t get on a soapbox because he’s too damn good at that.” (I guess I should note that Brooks is Jewish, even if that’s news only to Homer Simpson.) In that spirit, the closing credits of “Part I” tease a sequel including the segment “Hitler on Ice.” It’s assumed that the audience, without nudging, sees the ridiculousness of showing a genocidal monster pirouetting on skates.The first episode of “Part II” turns that brief joke into a full sketch with Barinholtz, Kroll and Sykes as sports announcers. Through the routine, their insults of the Nazi skater — “He’s a thug and bad for the sport” — grow sharper and more vulgar, as if to make clear that the depiction does not equal endorsement. It’s a funny bit, too, but funny for a more cautious, earnest time that prefers its problematic comedy more clearly underlined and bracketed.One advantage “Part II” has over its movie predecessor is the freedom of small scale. It can execute a one-joke premise and get out fast, as when it has Johnny Knoxville play the famously hard-to-kill czarist adviser Rasputin as the star of a Russian “Jackass.” (This also distinguishes it from Netflix’s “Cunk on Earth,” which can be screamingly funny but is condemned to repeat its Ali G-esque joke a little too long.)Still, “Part II” doesn’t entirely forget where it came from. A series of musical sketches featuring Kroll as a Jewish peasant selling mud pies during the Russian Revolution is the most Brooksian in style and setting. In a showstopping number, Kroll and Pamela Adlon fend off a murderous Cossack neighbor and duet about the trade-offs of city vs. shtetl life. (“Why seek out death and fear? / We’ve got plenty of it here!”)It’s just the dish to celebrate Mel Brooks’s legacy: Mud pie, à la mode. More