Place parchment paper on the work surface and put one of the chicken breasts on it.
Place your palm on top of the chicken breast and use a sharp knife moving parallel to your palm in between your hand and the table to slice the chicken in half the long way, creating two thinner chicken breast cutlets.
Place another piece of parchment on top of one of the chicken pieces and use a kitchen mallet or other heavy tool to gently pound the chicken to make it thinner and wider. Repeat with the remaining chicken pieces.
Get 3 shallow and wide bowls out. Put the breadcrumbs into one and mix in the lemon zest, black pepper, parsley, and half the lemon pepper seasoning into them.
In the next bowl, whisk the eggs, and in the third bowl, add the flour, a pinch of salt, and the remaining lemon pepper seasoning.
Fill a large frying pan with about 1/2 inch of oil. Bring to a medium high heat.
Grab one of the pieces of chicken and dredge it in the flour. Shake off excess. Then dip it into the eggs. Again, shake off excess. Now put it into the breadcrumbs and make sure to press the chicken into the breadcrumb mixture to coat it really well on all sides. Add it to the oil and cook to brown on both sides, repeating with all the chicken.
As they finish, transfer to a wire rack and set aside until ready to use. You don't need to put them in the fridge if you start making the sauce right away.