Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve ½ cup of pasta water, then drain the pasta and set aside.
In a large skillet over medium heat, melt the butter. Continue cooking the butter, stirring frequently, until it turns golden brown and has a nutty aroma, about 3-5 minutes.
Add the sliced mushrooms to the skillet and cook for about 5-7 minutes, or until they are browned and tender.
Stir in the minced garlic, thyme, salt, and black pepper. Cook for an additional 1-2 minutes until the garlic is fragrant.
Add the cooked pasta to the skillet along with the reserved pasta water and Parmesan cheese. Toss everything together until well combined and the pasta is coated in the brown butter sauce.
Serve immediately, garnished with fresh parsley and additional Parmesan cheese if desired.