Add the minced garlic and sliced mushrooms. Cook for 5-6 minutes, stirring occasionally, until the mushrooms release their moisture and turn golden brown.
Pour in the vegetable broth and heavy cream, then stir in the dried thyme, salt, and black pepper. Bring the mixture to a gentle simmer.
Break the fettuccine or linguine in half (optional, for easier stirring) and add it to the pot. Stir to submerge the pasta in the liquid. Cook uncovered for 10-12 minutes, stirring occasionally, until the pasta is al dente and the sauce has thickened. Add a splash of extra broth or water if the mixture becomes too thick before the pasta is cooked.
Remove from heat and stir in the grated Parmesan cheese until melted and the sauce is creamy. Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with chopped fresh parsley if desired. Enjoy your one-pot creamy mushroom pasta straight from the skillet!