In a large pot of salted boiling water, cook the fettuccine according to package instructions until al dente. Drain and set aside, reserving about 1/2 cup of the cooking water.
In a large skillet, heat the butter and olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.
Stir in the sliced mushrooms and cook for 5–7 minutes, or until they are golden brown and have released their moisture. Season with thyme, salt, and pepper.
Pour in the vegetable broth and bring to a simmer. Let it cook for about 3–4 minutes to reduce slightly.
Lower the heat and stir in the heavy cream and grated Parmesan cheese (if using), mixing well to combine. Add the cooked pasta to the skillet and toss everything together. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is achieved.
Taste and adjust seasoning as necessary. Let it simmer for an additional minute to heat through.
Serve the pasta warm, garnished with chopped fresh parsley and an extra sprinkle of Parmesan cheese if desired.