Cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain.
In a large pan, melt butter over medium heat. Add minced garlic and sauté until fragrant, about 1 minute.
Lower the heat and stir in heavy cream, Parmesan cheese, and reserved pasta water. Mix until smooth.
Add cooked pasta to the sauce and toss until fully coated. Season with salt and pepper to taste.
Serve warm, garnished with chopped parsley and extra Parmesan if desired.