01 - Pat the chicken breasts dry with paper towels. Season both sides generously with 1/2 teaspoon salt and 1/4 teaspoon black pepper, pressing the seasoning into the meat.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken breasts and cook for 6 to 7 minutes per side until golden brown and cooked through, reaching an internal temperature of 165°F. Transfer to a plate, cover loosely with foil, and let rest for 5 minutes before slicing thinly.
03 - Wipe the skillet clean if necessary. Return to medium heat and add butter. Once melted, add minced garlic and sauté for 1 minute until fragrant, being careful not to burn it.
04 - Pour in the heavy cream, stirring constantly to combine with the garlic. Bring to a gentle simmer, then reduce heat to low and cook for 2 to 3 minutes. Add Parmesan cheese, nutmeg if using, and 1/4 teaspoon black pepper. Stir continuously until the sauce is smooth and slightly thickened.
05 - Add spiralized zucchini noodles and 1/2 teaspoon salt to the sauce. Toss gently with tongs to coat evenly. Cook for 2 to 3 minutes until just tender but still crisp—do not overcook or the noodles will become watery.
06 - Return sliced chicken to the skillet and toss gently to coat with sauce and noodles. Heat through for 1 to 2 minutes. Serve immediately, garnished with chopped fresh parsley and extra grated Parmesan cheese.