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 4-5 minutes.
Add the sliced mushrooms to the skillet and sauté until they are browned and tender, about 5-7 minutes. Stir in the minced garlic and thyme, cooking for an additional 1-2 minutes until fragrant.
Add the cooked pasta to the skillet, tossing to combine with the mushrooms and brown butter. If the pasta seems dry, gradually add reserved pasta water until you reach your desired consistency.
Stir in the grated Parmesan cheese and season with salt and pepper to taste. Toss everything together until well combined.
Serve immediately, garnished with chopped parsley and additional Parmesan if desired.