Cut each chicken breast in half lengthwise to create two cutlets, four total.
In a small bowl combine 1 teaspoon salt, ¼ teaspoon pepper, and paprika. Evenly season both sides of the chicken with the spice mixture.
Heat a large skillet over medium heat. Once the pan is hot, add the olive oil. Add the chicken and cook until the surface is browned, about 5 for 6 minutes. Flip and cook until the internal temperature reaches 160 to 165ºF (71 to 74ºC), about 5 to 7 minutes.
Transfer to a plate and cover with foil to keep warm. Wash and dry the pan to use for making the alfredo sauce.
Pasta
In a large pot, bring 3 quarts of water to a boil. Add 1 ½ teaspoon salt, stir to dissolve.
Add the pasta and cook until al dente, about 10 to 12 minutes, or according to the manufacturer's directions. Use tongs to transfer to a colander—Reserve the starchy pasta water. While the pasta cooks, make the alfredo sauce.
Alfredo Sauce
Heat a large skillet over medium-low heat. Add butter. Once melted, add garlic and saute until fragrant, 30 to 60 seconds. Do not brown the butter or garlic.
Add the heavy cream, ½ teaspoon salt, and ½ teaspoon pepper, stir to combine. Bring the cream to a simmer over medium heat. Cook, frequently stirring, scraping the sides and bottom of the pan to make sure the cream does not curdle.
Reduce the sauce to about 1 cup, 10 to 12 minutes. It should be slightly thickened and be able to coat the back of a spoon.
Turn off the heat and stir in the parmesan cheese and nutmeg. If the sauce is too thick, add water or cream. Add 1 tablespoon at a time until you reach the desired consistency—season with salt and pepper to taste.
To Serve
Add the pasta to the sauce, gently tossing to combine.
Slice the chicken against the grain into ½-inch thick pieces.
Divide the pasta among bowls, top with sliced chicken and chopped parsley.
Notes
Make a Larger Batch: For 4 larger entree-sized portions, double the sauce and noodle ingredients. Reduce the sauce to 2 cups.
Diluting the Sauce: If the sauce concentrates too much, whisk in 1 tablespoon of hot pasta water or heavy cream at a time until desired consistency is reached.
Storing: Cool completely and store in an airtight container in the refrigerator for up to 5 days. Reheat in the microwave in 30-second intervals and stir until hot.