Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1 cup of pasta water, then drain the pasta and set aside.
In the same pot, melt the butter over medium heat. Add the minced garlic and red pepper flakes (if using), and sauté for about 1-2 minutes until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese until melted and smooth. If the sauce is too thick, add some reserved pasta water a little at a time until you reach your desired consistency.
Add the cooked pasta to the sauce, tossing to coat evenly. Season with salt and black pepper to taste.
Serve immediately, garnished with chopped fresh parsley.