Melt butter and olive oil in a large pan over medium-low heat. Meanwhile, put a pot of heavily salted water on to boil.
Add onions to the pan along with a pinch of salt and some pepper, and sweat them down until soft and transparent, about 10 minutes. Add garlic and cook for 2 minutes more. Add mushrooms along with another pinch of salt and cook until they give up all their water and begin to caramelize, 12 to 15 minutes. Don't worry if there are sticky brown bits on the bottom of the pan! They will add some good flavor after the next step.
A few minutes before you add the marsala wine, add your pasta to the boiling water. Cook it 2 minutes shy of al dente, about 6 to 8 minutes depending on the type of pasta you use. Drain.
Add the Marsala wine to the pan and scrape up any bits stuck to the bottom. Stir until most of the liquid has cooked off, about 5 minutes. Add in the mascarpone, the peas, more salt and pepper, and cook until the cheese melts into a silky sauce and the peas are warmed through.
Spoon mushroom marsala over noodles, top with parsley and more black pepper. Serve with Parmesan on the side.