Bring a large pot of salted water to a boil. Add the fettuccine or spaghetti and cook according to package instructions until al dente. Reserve 1 cup of the pasta water and then drain the rest.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant but not browned.
Add the sliced mushrooms to the skillet and cook for about 5 minutes until they are soft and browned.
Stir in the fresh spinach and cook until wilted, about 2-3 minutes.
Pour in the heavy cream and bring to a gentle simmer. Add the grated Parmesan cheese, stirring until melted and creamy. If the sauce is too thick, add reserved pasta water, a little at a time, until the desired consistency is reached.
Season the sauce with salt and black pepper to taste.
Add the drained pasta to the skillet, tossing to combine until the pasta is coated in the sauce.
Serve warm, topped with additional Parmesan cheese and red pepper flakes if desired.