Cook the pasta according to package instructions 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 diced onion and sauté for about 3-4 minutes until translucent.
Add the minced garlic and sliced mushrooms to the skillet. Cook for another 5-7 minutes until the mushrooms are browned and tender.
Stir in the dried thyme, salt, and black pepper. Cook for an additional minute to combine the flavors.
Pour in the Marsala wine and let it simmer for about 5 minutes, allowing it to reduce slightly.
Lower the heat and stir in the heavy cream and Parmesan cheese. Mix until the cheese is melted and the sauce is creamy. If the sauce is too thick, add some reserved pasta water to reach your desired consistency.
Add the cooked pasta to the skillet and toss to coat it in the sauce. Cook for another 2-3 minutes to heat through.
Serve immediately, garnished with fresh parsley.