Heat butter and olive oil in a large, deep skillet or pot over medium-high heat. Add the sliced mushrooms and cook until golden brown and any liquid has evaporated, about 6-8 minutes.
Add garlic and thyme to the mushrooms and cook for 1 minute until fragrant, stirring frequently.
Pour in the vegetable broth and heavy cream, then bring to a gentle boil.
Break the pasta in half and add it to the pot, making sure it's submerged in the liquid. Reduce heat to medium and cook, stirring frequently, for 10-12 minutes until the pasta is tender and the sauce has thickened.
If using spinach, stir it in during the last 2 minutes of cooking until wilted.
Remove from heat and stir in the Parmesan cheese. Season with salt and pepper to taste. Garnish with fresh parsley and serve immediately.