Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil and butter over medium heat. Add the sliced mushrooms and sauté for about 5-7 minutes, or until they are golden brown and tender.
Stir in the minced garlic, dried thyme, salt, and black pepper. Cook for an additional 1-2 minutes until the garlic is fragrant.
Pour in the heavy cream and bring the mixture to a simmer. Allow it to cook for 3-4 minutes, stirring occasionally, until the sauce thickens slightly.
Add the cooked pasta to the skillet, tossing to coat it in the creamy mushroom sauce. If the sauce is too thick, gradually add some reserved pasta water until you reach your desired consistency.
Stir in the grated Parmesan cheese until melted and well combined. Remove from heat.
Serve immediately, garnished with fresh parsley.