Mix together the flour, salt, pepper, and grated Parmesan. Rinse the chicken pieces in water. Dredge them thoroughly in the flour mixture.
Heat olive oil and 2 tablespoons of the butter in a large skillet on medium high heat. Add half of the chicken pieces to the skillet. Brown well on each side, about 3 minutes per side.
Remove the chicken from the pan and reserve on a plate. Repeat with remaining chicken. Cover plate with aluminum foil and keep warm in the oven while you prepare the sauce.
Add the chicken stock (or white wine), garlic, lemon juice, and capers to the pan. Reduce the sauce by half.
Whisk in the remaining 2 tablespoons of butter. Plate the chicken and serve with the sauce poured over the chicken. Serve over cooked pasta or mashed potatoes, if desired.
I used chicken cutlets, but this would also be good with chicken thighs. Make sure to cook the chicken until it reaches an internal temperature of 165ºF.Feel free to toss in some mushrooms and artichokes to the sauce.