In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
Melt butter in a Dutch oven over medium heat. Add mushrooms and onion, and cook, stirring occasionally, until mushrooms are tender and browned, about 8-10 minutes; season with salt and pepper, to taste.
Stir in garlic and thyme until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the Dutch oven.
Stir in chicken stock; season with salt and pepper, to taste. Bring to a boil; reduce heat and simmer, stirring occasionally, until reduced, about 7-9 minutes.
Stir in heavy cream until thickened, about 2 minutes.
Remove from heat. Stir in Parmesan; season with salt and pepper, to taste.
Stir in pasta until well combined.
Serve immediately, garnished with shaved Parmesan and parsley, if desired.