Bring a large pot of salted water to a boil. Cook pasta until al dente, drain, and set aside.
In a large skillet, heat olive oil and butter over medium heat. Add mushrooms and cook until browned.
Add onions and garlic, cooking until softened and fragrant.
Sprinkle in thyme, stir, and pour in white wine. Let it simmer until reduced by half.
Pour in broth and bring to a gentle simmer. Lower heat and stir in cream.
Add Parmesan, stirring until sauce thickens slightly. Taste and adjust seasoning with salt and pepper.
Toss cooked pasta in the sauce until well coated.
Serve hot, garnished with fresh parsley and extra Parmesan if desired.