Prepare the Chicken - Cut each chicken breast in half lengthwise to create two cutlets. There should be four pieces in total.
Season the Chicken - In a small bowl, combine 1 teaspoon salt, ¼ teaspoon pepper, and paprika. Evenly season both sides of the chicken with the mixture.
Cook the Chicken - Heat a large skillet over medium heat. Once hot, add the olive oil. Add the chicken and cook until the surface is browned, about 5 to 6 minutes. Flip and cook until the internal temperature reaches 160 to 165ºF (71 to 74ºC) on a thermometer, about 5 to 7 minutes.Transfer to a clean plate and cover with foil to keep warm. Remove any burnt bits and save the pan to make the alfredo sauce.
Cook the Pasta - In a large pot, bring the water to a boil. Add 1 ½ teaspoons salt and 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.
Make the Alfredo Sauce - Heat the skillet used to cook the chicken over medium-low heat. Add butter. Once melted, add garlic and saute until fragrant, 30 seconds. Do not brown the butter or garlic.Add the heavy cream, ½ teaspoon salt, and ½ teaspoon pepper, and stir to combine. Bring the cream to a simmer over medium heat. Cook, frequently stirring, scraping the sides and bottom to make sure the cream does not curdle. Reduce the sauce to about 1 cup, 10 to 12 minutes. It should be lightly thickened, coating a spoon.
Add the Cheese and Nutmeg - Turn off the heat and stir in the parmesan cheese and nutmeg. If the sauce is too thick, add the reserved pasta water, 1 tablespoon at a time, until the desired consistency is reached. Season with salt and pepper to taste.
To Serve - Add the pasta to the alfredo sauce, gently tossing to combine. Slice the chicken against the grain into ½-inch thick pieces. Divide the pasta among bowls and top with sliced chicken and chopped parsley.
Notes
Make a Larger Batch: Double the sauce and noodle ingredients for four larger entree-sized portions. Reduce the sauce to 2 cups.
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. If needed, add some water to loosen the sauce.