Cook the fettuccine according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.

While the pasta is cooking, heat the olive oil in a grill pan over medium-high heat. Season the chicken breasts with salt and pepper on both sides.

Place the chicken in the grill pan and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C). Remove from the pan and let it rest for a few minutes before slicing.

In the same pan used for the chicken, reduce the heat to medium and add the minced garlic. Sauté for about 1 minute until fragrant, being careful not to burn it.

Pour in the heavy cream and bring it to a gentle simmer. Stir occasionally and let it cook for 2-3 minutes until slightly thickened.

Add the grated Parmesan cheese and nutmeg to the cream, stirring until the cheese melts and the sauce is smooth. If the sauce is too thick, add a bit of the reserved pasta water until the desired consistency is reached.

Toss the cooked fettuccine in the Alfredo sauce until well coated. If needed, adjust the seasoning with additional salt and pepper.

Slice the grilled chicken and arrange it on top of the creamy fettuccine. Garnish with chopped parsley before serving.