01 - Bring a large pot of salted water to a boil. Cook the fettuccine according to package instructions until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
02 - While the pasta cooks, pat the chicken breasts dry with paper towels. Season both sides generously with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
03 - Heat olive oil in a large skillet over medium-high heat. Add chicken breasts and cook for 5 to 6 minutes per side until golden brown and cooked through (internal temperature reaches 165°F). Remove to a plate, let rest for 5 minutes, then slice thinly across the grain.
04 - In the same skillet, reduce heat to medium. Add butter and minced garlic. Sauté for 1 minute until fragrant but not browned.
05 - Pour in heavy cream and bring to a gentle simmer. Stir in Parmesan cheese until melted and smooth. Add nutmeg if using. Season with salt and pepper to taste, simmering for 2 to 3 minutes until slightly thickened.
06 - Add the cooked pasta to the skillet and toss to coat evenly in the sauce. If the sauce is too thick, add reserved pasta water 1 tablespoon at a time to reach desired consistency.
07 - Add sliced chicken to the pasta and toss gently to combine. Serve hot, garnished with chopped parsley and extra Parmesan cheese.