Cook the fettuccine or spaghetti according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
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 grated Parmesan cheese, salt, black pepper, and red pepper flakes (if using). Mix until the cheese is melted and the sauce is smooth.
Add the cooked pasta to the skillet, tossing to coat the noodles in the creamy sauce. If the sauce is too thick, gradually add some reserved pasta water until the desired consistency is reached.
Remove from heat and garnish with chopped fresh parsley before serving.