Place chicken breasts on a cutting board, cover with plastic wrap, and pound to an even thickness of about three-quarters of an inch. Season both sides with 1 teaspoon salt and 1/2 teaspoon black pepper.

Fill a large pot three-quarters full with water, bring to a rolling boil over high heat, and add a generous pinch of salt.

Heat 3 tablespoons of butter in a large skillet over medium-high heat until it foams and just begins to turn golden, then add the chicken breasts and sear for 6 to 7 minutes on the first side without moving them.

Flip the chicken and cook for another 5 to 6 minutes or until the internal temperature reaches 165°F. Remove the chicken to a cutting board and let it rest for 2 minutes before slicing.

Add the fettuccine to the boiling water and cook according to package directions, typically 9 to 12 minutes, until al dente. Reserve 1 cup of pasta cooking water before draining the pasta in a colander.

In the same skillet, melt the remaining 3 tablespoons of butter over medium heat. Add the minced garlic and cook for about 1 minute, stirring constantly, until fragrant and lightly golden.

Pour in the heavy cream and whole milk, stirring to combine. Bring the mixture to a gentle simmer over medium heat, then remove from the heat and stir in the grated Parmesan cheese until the sauce is smooth and creamy.

Stir in the fresh lemon juice and red pepper flakes if using. Taste and adjust the seasoning with additional salt and black pepper as needed.

Add the drained fettuccine directly to the sauce and toss gently with tongs, adding reserved pasta water a few tablespoons at a time until you reach the desired consistency. Divide the pasta among shallow bowls, top with sliced chicken, and garnish with chopped parsley.