"There was a time in cinema where crime films, particularly mafia and gangster related films, were way more common than they are now. Nowadays, you only get the Russian mafia as a villain in your actions. In those days, we also got a lot of comedies that mocked those too tough, too evil or too serious sides of characters in those gangster movies.
There were different kinds of them; many of them were parodies, but some were working both as an actual average crime drama story and a comedy simultaneously. There were satires that put a gangster in the center of different universes (like "Get Shorty"), there were direct spoof parodies ("Jane Austen's Mafia!") and then there are things like "Analyze This," where the mafia man had to get therapy."