Bring a large pot of water to a boil and season generously with salt. Once boiling, add the pasta and cook, stirring occasionally, until al dente. Reserve 1/2 cup of the pasta water and drain.
In a large skillet, melt the butter over medium heat. Cook, swirling occasionally, until the butter starts to foam and smells slightly nutty, this should take about 3 to 4 minutes. Add the mushrooms and cook, stirring occasionally, until mushrooms are tender and browned, about 5 minutes. Add the garlic and thyme, cook for 2 more minutes. Season with salt and black pepper, to taste.
Add the pasta to the skillet and stir in the reserved pasta water. Reduce heat to low and add half of the Parmesan cheese, stirring gently until melted. Add the remaining cheese and stir until melted. You can also use tongs to toss the pasta and cheese, so it doesn’t clump. Taste and season with salt and pepper, if necessary.
Transfer the pasta to plates or bowls and garnish with parsley, crushed red pepper flakes, and extra Parmesan cheese, if desired.