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.