Heat a large stock pot over medium-high heat. Melt on tablespoon of the butter in the hot pan.
Add onion, mushrooms, and pork. Stir and saute until pork is mostly cooked through, about 10 minutes. Remove meat and mushrooms to a bowl, and over with foil to keep warm. (It’s OK for onions to stay behind in the pan.)
Still over medium-high heat, melt second tablespoon of butter. Pour in uncooked rice, and stir and cook for about a minute.
Pour in one cup of broth. Stir often as broth simmers. When the broth is almost absorbed, pour in another cup and continue stirring. (It will take around 5 minutes for each cup to be absorbed before pouring in more.)
When the last bit of broth is almost completely absorbed, stir in the cooked pork, mushrooms, and the milk. Keep cooking and stirring until liquid is absorbed.
Stir in parmesan until melted. Turn off heat and serve.