Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant but not browned.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese, salt, black pepper, and red pepper flakes (if using). Cook for 2-3 minutes, stirring frequently, until the sauce thickens slightly.
Add the drained pasta to the skillet and toss to coat in the sauce. If the sauce is too thick, add some reserved pasta water a little at a time until the desired consistency is reached.
Remove from heat and garnish with chopped parsley before serving.