Start by placing the sliced chicken breasts between two sheets of plastic wrap. Using a meat mallet or rolling pin, gently pound them to an even thickness, about 1/2 inch. This helps the chicken cook evenly and remain tender. Season both sides generously with Kosher salt and freshly cracked black pepper.
In a shallow dish, add the all-purpose flour. Dredge each piece of chicken in the flour, ensuring they are well-coated. Shake off any excess flour and set the chicken aside.
In a large skillet, heat the extra-virgin olive oil over medium-high heat. Once hot, carefully add the floured chicken breasts in a single layer. Cook for about 4-5 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.
In the same skillet, reduce the heat to medium and add the unsalted butter. Once melted, add the minced garlic and sauté for about 30 seconds until fragrant. Be careful not to burn the garlic.
Next, add the thinly sliced lemon to the skillet, tossing gently to coat in the butter and garlic. Pour in the freshly squeezed lemon juice, stirring to combine. Let the sauce simmer for a minute to meld the flavors.
Return the cooked chicken to the skillet, spooning the lemon butter sauce over the top. Allow the chicken to heat through for another minute, absorbing all that wonderful flavor.
Remove the skillet from the heat and sprinkle with chopped fresh parsley for a burst of color and freshness. Serve immediately, drizzling more lemon butter sauce over the chicken if desired.