Set out 3 shallow bowls. In the first bowl, add the flour and season with the salt and pepper. In the second, add the eggs and whisk well. In the third, add the breadcrumbs, grated cheese, and minced parsley.
Slice the chicken breasts in half, lengthwise. Lay them out on your cutting board, lay a piece of plastic wrap over top of them, and using a meat mallet, pound them until they are 1/4 inch thick all througout.
Dredge each cutlet first into the flour, then the egg mixture, and then finally into the breadcrumbs. Make sure each side of the cutlets are coated well and set them aside once done.
In a large skillet, add enough oil until about 1/4 inch deep. Optionally drizzle in about 1-2 tablespoons of olive oil for flavor.
Set the heat to just above medium. You can tell when it's hot enough when a pinch of breadcrumbs bubbles when sprinkled into the hot oil.
Get a clean plate lined with paper towel ready to place your cooked cutlets on.
Lay your cutlets into the hot oil, away from you. You will need to do this in batches. Fry each side for about 2-3 minutes each. The cutlets are done when both sides are golden brown and crispy and the internal temperature reads 165°F.
Use tongs that have a good grip to remove the cutlets from the pan and lay them on the paper towel-lined plate. Silicone tongs get slippery and are not recommended. Metal tongs are much safer.
Serve immediately with fresh lemon wedges.