Begin by boiling a large pot of salted water. Cook the fettuccine or spaghetti according to package instructions until al dente. Reserve about 1 cup of pasta water before draining.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Add the minced garlic and sliced mushrooms to the skillet. Cook, stirring occasionally, until the mushrooms are browned and have released their moisture, about 5-7 minutes.
Pour in the vegetable broth and bring to a simmer. Cook for another 3-4 minutes, allowing the broth to reduce slightly.
Lower the heat and stir in the heavy cream, dried thyme, salt, and black pepper. Continue to cook for about 2-3 minutes until the sauce is heated through and slightly thickened.
Toss the cooked pasta into the sauce, adding a little reserved pasta water if needed to achieve your desired creamy consistency.
Stir in the grated Parmesan cheese and mix until well combined. Remove from heat.
Serve the pasta in bowls, garnished with freshly chopped parsley. Enjoy!