Place the chicken breasts between two pieces of plastic wrap, and using a meat mallet, pound the chicken breasts until about ½ inch thick. If the chicken breasts are very thick, you can also use a sharp knife to cut the chicken breasts in half to make cutlets.
Next, put together your dredging station. You'll need three shallow bowls or dishes. Place the gluten-free flour in one dish. In a second shallow bowl, mix the eggs and milk, and in the last bowl, whisk together the breadcrumbs, parmesan cheese, and seasonings to make the Italian breadcrumb mixture.
Before moving the chicken through the dredging station, salt, and pepper the chicken cutlets; this gives the chicken breast flavor before being covered with the flour.
Dip one chicken cutlet into the flour, shaking off any excess flour. Then dip it into the egg mixture, letting any extra egg drip off the chicken back into the bowl. Last, dip it into the breadcrumbs mixture. Set the breaded chicken cutlet on a plate and continue with the rest of the chicken cutlets.
Discard any unused flour, breadcrumbs, and egg mixture.
Over medium-high heat, heat the olive oil in a large, heavy-bottom saucepan until hot and shimmering. This means the oil is hot but not smoking hot.
Fry the breaded chicken cutlets in the hot oil. Don't crowd the pan; this will cause the breadcrumbs to get soggy or stick.
Fry the chicken for 4-5 minutes on each side until the coating is golden brown, juices run clear, and the chicken is no longer pink on the inside. The amount of time will ultimately depend on the thickness and size of the chicken breasts. The internal temperature of the pan-fried chicken cutlets should be 165 to be considered done and safe to eat.
Let the chicken rest for 2-3 minutes before using in another recipe.