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 the pasta water and drain the rest.
2. While the pasta is cooking, heat olive oil and butter in a large skillet over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant.
3. Add the sliced mushrooms to the skillet. Cook for 5-7 minutes, stirring occasionally, until the mushrooms are golden and tender.
4. Pour in the vegetable broth, scraping up any browned bits from the bottom of the skillet. Let it simmer for a couple of minutes to reduce slightly.
5. Reduce the heat to low and stir in the heavy cream. Allow it to heat through, then add the grated Parmesan cheese, stirring until melted and the sauce is smooth.
6. Season with salt and pepper to taste, and add a pinch of red pepper flakes if using.
7. Toss the cooked pasta into the sauce, adding reserved pasta water as needed to reach your desired consistency. Stir in the chopped parsley and give it a final toss.
8. Serve immediately, garnished with additional Parmesan and parsley if desired.

This recipe is all about intuition and taste—two guides that have served me well in my culinary journey. Remember, the key is to taste as you go, adjusting the seasoning to suit your preference.