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.
Notes
If capers aren’t available or not your thing, olives are the next best choice. They are both brined and provide a similar salty piquant taste. Use green olives, then thinly slice or chop them into smaller pieces. Kalamata would work as well for this dish.