1. Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
2. In a large skillet, heat olive oil over medium heat. Add the sliced mushrooms and cook until golden brown, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant.
3. Pour in the heavy cream and broth, stirring to combine. Bring the mixture to a gentle simmer and add the grated Parmesan cheese, stirring until smooth.
4. Season with dried thyme, salt, and pepper. Let the sauce simmer for 5 minutes, allowing it to thicken slightly.
5. Add the cooked pasta to the skillet, tossing to coat in the sauce. If needed, add a bit of the reserved pasta water to reach your desired sauce consistency.
6. Garnish with freshly chopped parsley before serving, adding a pop of color and freshness to the dish.

As you cook, remember the joy of tasting and adjusting as you go, a practice my Abuela always encouraged. Cooking is an art, and your palate is the most important guide.