Start by patting the chicken breasts dry with paper towels. This helps to achieve a beautiful sear. Cut each breast in half lengthwise to form two thinner cutlets. Season the pieces generously with kosher salt and ground black pepper.
In a large bowl, place the all-purpose flour. Dredge the seasoned chicken cutlets in the flour, ensuring they are well coated. Shake off any excess flour to prevent clumping during cooking.
Heat a large nonstick skillet over medium heat and add the olive oil and 2 tablespoons of unsalted butter. Swirl the pan until the butter is melted and bubbling, indicating it's ready for the chicken.
Carefully place the coated chicken cutlets in the skillet. Cook them for about 3 to 4 minutes on each side, or until they turn a beautiful golden brown and reach an internal temperature of 165°F. Remove the chicken from the skillet and set it aside on a plate.
Reduce the heat to low and add the remaining 4 tablespoons of unsalted butter to the skillet. Once melted, add the garlic and sauté for 30 to 60 seconds, just until it's fragrant but not browned. You want to extract all that lovely flavor!
Next, stir in the minced fresh parsley. This will brighten the garlic sauce and give it some lovely color.
Return the chicken to the skillet, spooning the fragrant garlic butter over the top of each piece. Let it cook for an additional minute to meld the flavors.
Finally, remove the skillet from the heat. Sprinkle the grated Parmesan cheese generously over the chicken, allowing it to melt slightly from the residual heat.
Serve your Garlic Knot Chicken immediately with fresh lemon wedges on the side. This adds a wonderful zest when squeezed over the chicken just before enjoying.