Place chicken breast (one at a time) between two pieces of parchment paper. Using a mallet, pound the chicken until it is ¼ inch in thickness. Repeat with the other chicken breast.
Start with 2 dinner plates. Beaten egg on the first plate, and parmesan, panko crumbs, kosher salt and pepper (mixed well) on the second plate. Keep one hand clean and free of assembly ingredients.
One at a time, dredge in flour and shake off excess. Proceed with dipping the chicken in the egg mixture, ensuring the chicken is coated well and gently shaking off excess egg. Place chicken on the last plate and with your free hand, sprinkle panko and parmesan mixture over chicken until well-coated.
Add 1½ tablespoons olive oil and 1 tablespoon butter to a skillet. Add one breaded chicken cutlet and cook first side for two minutes or until golden brown then carefully flip. Once both sides are golden brown, remove and place on a wire rack. Add more olive oil and butter as needed.
To serve, place whole or sliced chicken cutlet on a plate. Squeeze lemon wedge over the top followed by pouring tonnato sauce over the cutlet or serve in a ramekin if preferred to dip.