Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of 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. Reduce the heat to low and 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 reserved pasta water until you reach the desired consistency.
Remove from heat and garnish with chopped parsley before serving.