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 over medium heat. Add the chopped onion and sauté for about 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet. Cook for another 5-7 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Stir in the dried thyme, salt, and black pepper. Cook for an additional minute to combine the flavors.
Pour in the heavy cream and bring the mixture to a gentle simmer. Let it cook for 2-3 minutes until slightly thickened.
Add the cooked pasta to the skillet, tossing to coat in the creamy mushroom sauce. If the sauce is too thick, add a little reserved pasta water to reach your desired consistency.
Stir in the grated Parmesan cheese until melted and well combined. Adjust seasoning if necessary.
Serve immediately, garnished with fresh parsley.