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 minced garlic to the skillet and sauté for 1 minute until fragrant, stirring frequently to prevent burning.
Add the sliced cremini mushrooms to the skillet. Season with salt, black pepper, and dried thyme. Cook for 8-10 minutes, stirring occasionally, until the mushrooms are browned and tender.
Reduce the heat to low and pour in the heavy cream. Stir to combine and let the mixture simmer gently 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 fettuccine pasta to the skillet and toss gently to coat the pasta evenly with the creamy mushroom sauce.
Remove from heat and sprinkle the chopped fresh parsley over the pasta.
Serve immediately, garnished with extra Parmesan cheese if desired.