Heat 2 tablespoons of extra-virgin olive oil in a large skillet over medium-high heat. Season the boneless, skinless chicken breasts with kosher salt and freshly ground black pepper. Cook each piece for about 6-8 minutes per side, or until golden brown and cooked through. The internal temperature should reach 165°F. Transfer the chicken to a cutting board and let it rest before slicing into bite-sized pieces.

In the same skillet, add 2 cups of low-sodium chicken broth and 2 cups of whole milk along with 2 finely chopped garlic cloves. Season with additional salt and pepper to taste. Bring this mixture to a gentle simmer over medium heat.

Add 8 ounces of fettuccine to the simmering liquid, stirring frequently to prevent it from sticking. Cook the pasta for about 8-10 minutes, or until it's barely al dente.

Once the pasta is al dente, reduce the heat to low and stir in 1 cup of finely grated Parmesan cheese and 3/4 cup of heavy cream. Allow the sauce to simmer gently, mixing well until it thickens slightly and the cheese has melted completely.

Remove the skillet from heat and gently fold in the sliced chicken, ensuring it's evenly coated with the creamy Chicken Alfredo sauce. If desired, garnish with fresh parsley before serving.