Next, we prepare the chicken. We rinse them and then place on the wax paper lined counter. Using kitchen scissors, we halve each breast lengthwise and then again crosswise. We trim away any fat or unmentionables, making sure they are in one layer on the wax paper. We wash our hands well and cover the chicken pieces with another piece of wax paper. We pound them with our mallet to even their thicknesses and get them as thin as we can. We wash up again for good measure.
On a plate we place a piece of wax paper and pour on the flour. We add some salt and pepper to taste. In a bowl we lightly beat the eggs with the cheese and add some freshly ground black pepper.
In a large frying pan, we heat 2 tablespoons of olive oil over medium heat. While it is heating, we place 4 cutlets, one at a time, first into the flour mixture, coating them lightly, then the egg mixture, then again in the flour mixture, and finally in the egg mixture. As a cutlet is done, we place into the hot oil. We pan-fry for 2 minutes, turning when the bottom is nicely brown. We are sure to keep our hands very clean to avoid cross-contamination. We continue to cook the cutlets on the other side for another couple of minutes and then we drain on a paper-towel-lined plate.
While we do the remaining batches, we place the chicken into the oven on a foil-lined cookie sheet to be sure they are cooked through and hot. We repeat the double-dipping with the remaining chicken cutlets, adding more oil as necessary, until all of the pieces are cooked.
Once all of the chicken is pan-fried and while it is finishing cooking in the oven, we turn off the heat on the frying pan. We add the parsley, the butter, lemon juice, a little salt and pepper to the oil still in the pan (around ½ tablespoon) and stir.
We remove the chicken from the oven, place on a serving platter, and pour the sauce on top.