Cook Garlic: In a large pot, heat olive oil over medium heat. Add garlic and sauté for about 1 minute, until fragrant.
Add Pasta and Liquids: Add the pasta, chicken or vegetable broth, and heavy cream to the pot. Bring to a boil, then reduce heat and simmer, uncovered, stirring occasionally to prevent the pasta from sticking.
Add Cheese and Veggies: Once the pasta is nearly done (about 10 minutes), stir in the grated Parmesan cheese, mushrooms, and spinach, if using. Continue cooking until the pasta is al dente and the sauce has thickened.
Season and Serve: Season with salt and pepper to taste. Serve hot, garnished with extra grated Parmesan if desired.