Bring a large pot of salted water to a boil. Cook the fettuccine according to package instructions until al dente. Drain and set aside.
In a large skillet, heat butter and olive oil over medium heat. Add the minced garlic and sauté for 1 minute until fragrant.
Add the sliced mushrooms, salt, black pepper, and thyme. Cook for 5-7 minutes, stirring occasionally, until the mushrooms are tender and golden brown.
Pour in the heavy cream and broth, stirring to combine. Bring to a gentle simmer and cook for 3-4 minutes, allowing the sauce to thicken slightly.
Stir in the Parmesan cheese and red pepper flakes (if using). Mix well until the cheese is melted and the sauce is smooth.
Add the cooked fettuccine to the skillet, tossing to coat the pasta evenly with the sauce.
Sprinkle with fresh parsley, give it one final toss, and remove from heat.
Serve immediately with extra Parmesan cheese on top and enjoy!