Heat a skillet to medium-high and add the olive oil. Sprinkle the 4 chicken cutlets with salt on both sides. Pour the flour into a wide shallow bowl and lightly dredge the chicken until fully coated. Shake off excess. Brown the cutlets for about 4 minutes on each side, until they reach 165 degrees internally. If needed, cook the chicken in batches to prevent overcrowding the pan. Once all of the chicken is brown, place on a wire rack while you prepare the sauce. Turn the heat down slightly to medium. If needed, drain off any excess oil, then add the shallots and garlic and sauté for about 2 minutes. Add the capers and sauté for about 1 minute more. Add the white wine to deglaze. Use a wooden spoon to scrape brown bits stuck to the bottom of the pan. Add the lemon juice and the chicken broth and reduce for 5 minutes. It will be a somewhat loose sauce so don't worry if it hasn't thickened much. Turn the heat to low and add the butter. Stir it in to emulsify it with the sauce.Return the chicken to the pan and toss it to fully coat both sides. Finish with fresh parsley.