Place the chicken breasts between two sheets of plastic wrap. Use a meat mallet or rolling pin to gently pound the chicken to an even thickness, about ½ inch.
Season both sides of the chicken breasts with kosher salt and ground black pepper.
Place the all-purpose flour in a shallow dish. Dredge each chicken breast in the flour, shaking off any excess.
In a large skillet, heat the olive oil over medium-high heat. Once hot, add the floured chicken breasts. Cook for 5-6 minutes on each side until golden brown and cooked through (165°F internal temperature).
Remove the cooked chicken from the skillet and set aside. Reduce heat to medium, add 4 tablespoons of unsalted butter. Once melted, add the finely chopped garlic and sauté for 1-2 minutes until fragrant.
Stir in the minced fresh parsley and grated Parmesan cheese into the garlic butter sauce. Mix until the cheese melts and sauce is creamy.
Return the chicken breasts to the skillet, spoon the garlic butter sauce over them, and simmer for a couple of minutes to absorb flavors.
Transfer the Garlic Knot Chicken to a serving platter. Drizzle any remaining sauce on top and serve with lemon wedges, if desired.