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 until melted and smooth.
Season the sauce with salt, black pepper, and red pepper flakes if using. If the sauce is too thick, add a little reserved pasta water to reach desired consistency.
Add the cooked pasta to the skillet and toss to coat in the creamy sauce. Cook for an additional 2-3 minutes, allowing the pasta to absorb some of the sauce.
Remove from heat and garnish with chopped parsley before serving.