While the sauce cooks, cut each chicken breast in half lengthwise and place each piece of chicken into a large plastic zip-top bag. Use a mallet to gently pound them so they are about ½” thick. Be careful that the meat does not break.
To bread the chicken, set up three separate bowls. Place the flour in the first bowl. In the second bowl beat the eggs. In the third bowl combine the fine breadcrumbs, panko breadcrumbs, Parmesan cheese, lemon zest, garlic power, onion powder, and parsley.
Add enough vegetable oil to a large frying pan so that it is ¼-inch deep. Heat until the surface of the oil is shiny.
Take a piece of chicken and dredge through the flour then the egg mixture and then the breadcrumbs.
Fry until the chicken is completely cooked through and golden brown on each side, about 8 minutes.
Remove to a paper towel-lined plate to drain the excess oil. Continue the process until all of the chicken is fried.