In the Shakespeare Writers' Room, Francis Bacon suggests a musical version of Hamlet. This is a reference to Mel Brooks' stage/film musical 'The Producers', in which Max Bialystock produces a Hamlet musical called "Funny Boy." It also closely resembles the 2015 Broadway musical "Something Rotten!", which also deals in part with Shakespeare suffering from writer's block.
The voice Nick Kroll uses as the Russian peasant is the same voice he uses as Gil Faison from his and John Mulaney's hit Broadway show 'Oh, Hello!'