Heat butter and oil in a large deep skillet or pot over medium-high; cook mushrooms 6-8 minutes until golden brown and moisture evaporates, stirring infrequently to caramelize.
Cook shallot 2 minutes until softened; add garlic and thyme and cook another minute until fragrant.
Add optional wine; simmer 2 minutes to cook off alcohol.
Add pasta and broth, keeping pasta mostly submerged; season with salt and pepper, boil, and reduce to a simmer.
Cook 10-12 minutes, stirring frequently, until pasta is al dente and most liquid absorbed.
Reduce heat to low; stir in cream, Parmesan, and optional nutmeg until creamy and cheese fully melted.
Adjust seasoning; garnish with fresh parsley and extra Parmesan and serve immediately.