Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
In a large skillet, heat the butter and olive oil over medium heat until melted and hot.
Add the sliced mushrooms to the skillet and sauté for 6-8 minutes, stirring occasionally, until they release their moisture and become golden brown.
Add the minced garlic, salt, black pepper, and dried thyme to the mushrooms. Cook for an additional 1-2 minutes until fragrant.
Pour the heavy cream into the skillet and stir to combine. Bring the mixture to a gentle simmer and cook for 3-4 minutes until the sauce thickens slightly.
Stir in the grated Parmesan cheese until melted and the sauce is creamy.
Add the cooked pasta to the skillet and toss well to coat the pasta evenly with the creamy mushroom sauce.
Remove from heat and sprinkle the chopped fresh parsley over the pasta. Toss gently to combine.
Serve immediately, garnished with extra Parmesan cheese if desired.