Heat the olive oil in a large pot or Dutch oven over medium heat. Add the sliced mushrooms and cook until they release their liquid and begin to brown, about 6 to 8 minutes.
Add the minced garlic, thyme, salt, and pepper to the pot. Cook for 1 minute until the garlic is fragrant.
Add the vegetable broth and the dry pasta to the pot. Bring the mixture to a boil.
Reduce the heat to medium-low, cover the pot, and simmer for 10 to 12 minutes, stirring occasionally, until the pasta is cooked al dente and most of the liquid is absorbed.
Remove the pot from the heat. Stir in the heavy cream and grated Parmesan cheese until the sauce is smooth and creamy.
Taste and adjust salt and pepper if needed. Serve immediately, garnished with fresh parsley.
Notes
For a Tuscan flavor, add 1/2 cup of fresh spinach during the last 2 minutes of cooking until wilted.
Use high-quality Parmesan cheese for the best sauce texture.
If the sauce is too thick after adding the cream, add a splash of reserved pasta water or extra broth to thin it slightly.