Cook the Pasta: Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente. Reserve 1 cup of pasta water, then drain the pasta and set aside.
Sauté Mushrooms: In a large skillet, heat the olive oil over medium heat. Add the sliced mushrooms and sauté for about 5-7 minutes or until they are golden brown and tender.
Add Garlic and Spinach: Add the minced garlic and dried thyme to the skillet, cooking for an additional 1-2 minutes until fragrant. Stir in the fresh spinach and cook until wilted, about 2 minutes.
Create the Cream Sauce: Lower the heat, then pour in the heavy cream. Stir well to combine. Allow the cream to simmer for 2-3 minutes to thicken slightly.
Mix in Parmesan: Sprinkle in the grated Parmesan cheese, mixing until melted and smooth. Use a splash of the reserved pasta water if the sauce needs thinning.
Combine Pasta and Sauce: Add the cooked pasta to the skillet, tossing everything together to coat the pasta thoroughly in the creamy sauce. Season with salt and pepper to taste.
Serve: Plate the pasta and garnish with freshly chopped parsley and a sprinkle of extra Parmesan cheese, if desired.