Cook fettuccine in a large pot of salted boiling water according to package directions until al dente. Drain, reserving ¼ cup pasta water.
In a large skillet over medium heat, melt butter and sauté minced garlic until fragrant (about 1 minute).
Pour in heavy cream, stir, and bring to a simmer. Cook for 2–3 minutes until slightly thickened.
Reduce heat to low. Stir in Parmesan cheese slowly until melted and smooth.
Add pasta to sauce, tossing to coat. If sauce is too thick, add reserved pasta water a tablespoon at a time until desired consistency.
Season with salt and black pepper to taste.
Serve immediately, garnished with optional chopped parsley.