Using a meat mallet or rolling pin, pound the chicken breasts thin (⅓ inch thick). Season both sides with salt and pepper.

Place flour in a shallow dish and dredge both sides of the chicken breasts with it until fully covered. Shake any excess flour and place the chicken breasts on a plate.

Heat a large skillet over medium-high heat and add the olive oil and one tablespoon of butter. Once the butter has melted, place the chicken breasts in a single layer and brown for 4 minutes on one side, and 4 additional minutes on the other side. Transfer to a plate and keep warm (cover with foil)

Using the same skillet, reduce the heat to medium and add the garlic. Cook for 30 seconds, just until fragrant. Be careful not to burn it. Pour in the white wine to deglaze the pan, scraping any leftover brown bits from the bottom. Add the chicken broth and lemon juice, and simmer until reduced by half, about 3-4 minutes.

Once reduced, add the rest of the butter and the lemon zest. Stir gently until all the butter has been incorporated into the sauce. Season with salt and pepper if needed.

Return the chicken breasts to the skillet and add one tablespoon of chopped parsley and the red pepper flakes. Cover the chicken with the sauce and cook for about 2 minutes until heated through. Serve with the remaining tablespoon of fresh parsley on top.