I like the structure of the game 2048 https://github.com/gabrielecirulli/2048 and I think it will be highly instructive for you since it implements the MVC pattern without using a framework, and you want to be framework agnostic. 2048 is simple enough that it's an accessible introduction to software design.

Daniel Janus wrote a great analysis of the source code and architecture; I highly recommend reading it: http://blog.danieljanus.pl/blog/2014/04/02/2048/