01 - Pat the chicken breasts thoroughly dry. Season both sides with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Place the seasoned chicken breasts in the hot skillet and cook for 6–7 minutes per side, until they are golden brown and fully cooked through (an instant-read thermometer should register 165°F internally). Transfer the cooked chicken to a plate, cover loosely, and allow it to rest for 5 minutes before thinly slicing.
02 - If necessary, wipe the skillet clean. Add 2 tablespoons unsalted butter to the skillet and melt over medium heat. Introduce 3 cloves of minced garlic and sauté for 1 minute until it becomes fragrant.
03 - Pour in 1 cup of heavy cream, stirring to combine. Bring the mixture to a gentle simmer, then reduce the heat to low and continue to cook for 2–3 minutes. Stir in 1/2 cup grated Parmesan cheese, 1/4 teaspoon nutmeg (if using), and 1/4 teaspoon black pepper. Stir continuously until the sauce is smooth and slightly thickened.
04 - Add 4 spiralized medium zucchini noodles and 1/2 teaspoon salt to the finished Alfredo sauce. Gently toss the noodles to coat them evenly and cook for 2–3 minutes, until they are just tender but still maintain a slight crispness. Avoid overcooking, as this can make the zucchini watery.
05 - Return the thinly sliced cooked chicken to the skillet with the sauced zucchini noodles. Gently toss to ensure the chicken is thoroughly coated and heated through, which should take 1–2 minutes. Serve the dish immediately, garnished with 2 tablespoons chopped fresh parsley and additional grated Parmesan cheese, as desired.