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 the mushrooms are golden brown and have released their moisture.
Add the minced garlic, salt, black pepper, and dried thyme to the mushrooms. Cook for 1-2 minutes until fragrant.
Pour in the heavy cream 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 smooth.
Add the cooked fettuccine to the skillet and toss to coat the pasta evenly with the creamy mushroom sauce.
Remove from heat and sprinkle with chopped fresh parsley before serving.