Watch Gaidai, Ryazanov or Danelia (who also did some great comedies, like Mimino), you won't get too wrong.

https://en.wikipedia.org/wiki/Leonid_Gaidai https://en.wikipedia.org/wiki/Eldar_Ryazanov https://en.wikipedia.org/wiki/Georgiy_Daneliya

Edit: probably not so short, just regular stories... so maybe not what you're looking for.

Gogol essentially invented the Russian novel, and most of his stories are very comedic. Here's a particular favourite:

https://en.wikipedia.org/wiki/The_Tale_of_How_Ivan_Ivanovich...

and the story that influenced me to move to Russia: https://en.wikipedia.org/wiki/The_Government_Inspector

Whatever you do, don't miss The Nose, there's even a brilliant pinscreen animation adaptation: https://www.openculture.com/2014/09/animation-of-nikolai-gog...

[1] https://en.m.wikipedia.org/wiki/Fitil

[2] https://en.m.wikipedia.org/wiki/Yeralash

12 Chairs + Golden Calf by Ilf and Petroff; A dog's heart and Master and Margarita by Boulgakoff. I've heard Zosh'enko was also considered very funny at the time, but I'm not sure how well his stuff has aged..

"Davydov and Goliath" and "Golden button" are coming to mind.