Bring a large pot of salted water to a boil. Cook the 12 oz fettuccine until al dente, 10 to 11 minutes. Reserve 1/4 cup pasta water before draining.

Melt the 4 tbsp unsalted butter in a large skillet over medium-low heat. Add the 3 cloves minced garlic and cook for 2 minutes until fragrant and pale gold.

Pour in the 2 cups heavy cream and raise to medium heat. Simmer for 4 to 5 minutes, stirring occasionally, until slightly thickened.

Reduce heat to low. Whisk in the 1.5 cups Parmesan in small additions, then stir in the 1/2 tsp salt, 1/4 tsp black pepper, and 1/4 tsp nutmeg until smooth and glossy, about 2 minutes.

Add the drained fettuccine and toss over low heat for 1 minute, adding the 2 tbsp reserved pasta water as needed. Divide into warm bowls, spoon extra sauce over the top, and garnish with the 1 tbsp chopped parsley and extra Parmesan.