Add the butter to a small saucepan and heat over medium-low heat. Melt and gently cook until the butter is deep golden in color and smells nutty.
Heat the olive oil in a wide and deep skillet over medium-high heat. Cook the onion, garlic and sliced Swiss chard stalks until softened, about 5 minutes.
Stir in the mushrooms and continue cooking for about 10 minutes or until the mushrooms are cooked, stirring frequently.
While the mushrooms are cooking, boil water for the pasta. Undercook the pasta slightly (it will finish cooking in the sauce).
Once the mushrooms are cooked, stir in the Swiss chard leaves into the skillet with the vegetables and cook until wilted, about 1 minute.
Turn up the heat to high and wait until the pan is sizzling hot. Pour the white wine into the pan and cook, scratching the browned bits off the bottom of the pan. Simmer until the raw alcohol smell is gone, about 1-2 minutes. Stir in the broth and cook for another 1-2 minutes.
Add the pasta to the skillet and cook, tossing all the time, until the pasta is fully cooked and the sauce is clinging to the noodles. Stir in the cheese and parsley.
Serve with the browned butter, extra parmesan and black pepper.