In a large deep skillet or wide pot, heat the butter and olive oil over medium heat until melted and hot.
Add the sliced mushrooms to the pot and sauté for 5-6 minutes, stirring occasionally, until they are browned and softened.
Add the minced garlic, dried thyme, salt, and black pepper to the mushrooms and cook for 1 minute until fragrant.
Add the broken fettuccine pasta to the pot, then pour in the vegetable broth. Stir to combine and make sure the pasta is submerged in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered for 12-15 minutes, stirring occasionally, until the pasta is cooked al dente and most of the liquid has been absorbed.
Stir in the heavy cream and grated Parmesan cheese, mixing well until the sauce is creamy and coats the pasta evenly.
Cook for an additional 2-3 minutes on low heat, stirring frequently, until heated through and slightly thickened.
Remove from heat and sprinkle chopped fresh parsley over the pasta before serving.