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.
While the pasta cooks, heat the butter and olive oil together in a large skillet over medium heat until melted and hot.
Add the sliced mushrooms to the skillet and sauté for 6-8 minutes, stirring occasionally, until the mushrooms are golden brown and tender.
Add the minced garlic, salt, black pepper, and dried thyme to the mushrooms. Cook for 1-2 minutes until fragrant, stirring frequently to avoid burning the garlic.
Pour the heavy cream into the skillet with the mushrooms and stir to combine. Bring the mixture to a gentle simmer and cook for 3-4 minutes until the sauce thickens slightly.
Reduce the heat to low and stir in the grated Parmesan cheese until melted and the sauce is creamy.
Add the cooked fettuccine pasta to the skillet and toss gently to coat the pasta evenly with the creamy mushroom sauce.
Remove the skillet from heat and sprinkle the chopped fresh parsley over the pasta. Toss once more to combine.
Serve the creamy mushroom pasta immediately, garnished with extra Parmesan cheese if desired.