After playing doctors (“House”) and presidential aides (“Designated Survivor”) in his most recent TV roles, Kal Penn exercises his comedic chops in the new NBC fall series “Sunnyside” — which the network, in a rare move, has made available for review months before its premiere.

The effect is refreshing. Penn has a dream role as a recognizably contemporary character — the disgraced politician on a redemption tour — as former New York City Councilman Garrett Modi, who squandered his fortunes in a drunken YouTube video that shows him staggering across the BQE, vomiting on a cop car and attempting to bribe a police officer.

Charlie Sheen would be proud. Winning!

Having lost everything — and realizing moving back home with your parents when you’re in your 40s is too pathetic — Modi (Penn’s real last name) throws himself on the mercy of his successful physician sister (Kiran Deol), moving in with her as he plots his cheesy comeback and eventual reelection.

He starts incrementally, selling his sad image as “the BQE puker” to online influencers who pay him $50 an hour to pose for selfies where they get to imitate him hurling. Eventually, he is lured by a group of immigrants that want his professional help in passing the nationalization test so they can become American citizens. This motley crew meets in a Queens bar and includes an Ethiopian cab driver, obscenely wealthy Asian siblings, an impatient Romanian millennial and a middle-aged Dominican woman who has about 10 different jobs.

The rest of the show is about the real political education of Garrett Modi. As the immigrants do their exam prep, Modi learns about their difficulties in attaining the American dream. For example, Ethiopian cab driver Hakeem (Samba Schutte) was a cardiothoracic surgeon in his country but can’t get certified in the US (citizenship should help). An unexpected crisis among the group forces Modi to reach out to his real political contacts, making those dreams of citizenship more feasible.

Fortunately, “Sunnyside” doesn’t wear its earnestness on its sleeve. Penn, born in Montclair, NJ, and the son of immigrant parents, is a co-writer on the series (with Matt Murray) and infuses his character with natural warmth, even if Modi is a jerk. The supporting cast has a few standout performances (Diana Maria Riva as multitasking Griselda) and one weak link (Moses Storm, as the resident millennial, hits his punch lines too hard). Poppy Liu and Joel Kim Booster score the biggest laughs as the tragically hip siblings. While getting quizzed about Constitutional amendments, Booster looks up from his booklet and cries out in despair, “I don’t know why everyone expects me to learn things now. It’s not my brand!”

NBC has only three new series this fall: “Bluff City Law” with hasn’t-had-a-hit-in-decades Jimmy Smits, “Perfect Harmony” with “West Wing” leftover Bradley Whitford and “Sunnyside.” With his easy charm, smart script and diverse cast, Penn may help the network deliver something that’s been eluding it — a comedy that’s timely and winning.