On a flat dish, combine kosher salt, pepper, lemon pepper and 2 tbsp of the flour. Coat chicken cutlets in flour mixture and place on a plate. Sprinkle half of the lemon zest over cutlets.
Heat oil in a large skillet over medium heat. Brown chicken until cooked through, about 7 minutes, turning once. Transfer to a fresh plate.
In a bowl, whisk lemon juice, chicken broth, capers, garlic and remaining zest until smooth. Pour into skillet with drippings and whisk until combined. Add half-and-half, if desired. Return chicken to pan and heat through, 2 minutes. To serve, spoon sauce over cutlets and garnish with parsley, if desired.
