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.
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.
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.
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.
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.