Heat butter and oil in a large deep skillet or pot over medium-high; cook mushrooms 6-8 minutes until golden brown and liquid evaporates.
Add garlic and thyme; cook 1 minute, stirring frequently, until fragrant.
Add broth and cream; bring to a gentle boil.
Halve pasta and submerge in pot; reduce heat to medium and cook 10-12 minutes, stirring frequently, until tender and sauce thickens.
Add optional spinach during last 2 minutes to wilt.
Off heat, stir in Parmesan; season with salt and pepper, garnish with fresh parsley, and serve immediately.