Something new? Pfft. I wish. It's like that kind of comedy just dropped off the map; everything I see even in the category of "comedy" in the last few years is usually some sort of Romcom, or better categorized as something else (like Action for a Marvel hero movie).
Though you did say League of Extraordinary Gentlemen so perhaps some of the Marvel films would do it. They are fairly humorous. Especially the Antman movies.
Outside of movies, there's a bunch of current cartoons on YouTube that are great, but without any kind of schedule for uploads like Helluva Boss and Digital Circus. Hazbin Hotel is starting January 19th on Amazon, too.
League of Gentlemen, not league of extraordinary gentlemen. If you haven't seen it, you're in for a treat. It's some of the raunchiest piss your pants stupid funny stuff you'll ever see. https://m.imdb.com/title/tt0184135/
Call me jaded, but whenever anyone shares some post/youtube/tiktok of someone telling some crazy story, I just never believe it unless they got the receipts. One video that lives rent-free in my head is called “Ghost in the Stalls”, it was shared by my friends in college and they all loved it and I’m over here just confused as to why they think it’s a real story. Even as a fake story it was not funny because it was full of not-so-clever punlines.
I searched for "Ghost in the Stalls" It's a video of a guy talking to the camera... I switched to the animated version, I don't know why I thought it could be funny at least more than the guy just talking... it wasn't.
I bet the guy is an aspiring writer, it's bad, don't waste your time.