Prepare the chicken cutlets: Place a chicken breast onto the cutting board, then with one hand on top of the breast, use a chef’s knife with the other hand to slice the breast in half horizontally (crosswise), making 2 thinner chicken breast cutlets. Repeat with the remaining chicken breasts.
Pound the chicken: Place the chicken cutlets between sheets of plastic wrap or parchment paper and pound to about ⅓ inch thick using a mallet or the bottom of a small pot.
Season the chicken: In a small bowl, mix ½ teaspoon salt with ½ teaspoon freshly ground black pepper. Line a large baking sheet with parchment paper, then arrange the chicken on it. Season both sides evenly with the salt and pepper mixture.
Set up the breading station: You’ll need three wide, shallow bowls. Add the flour to the first. In the second, whisk together the eggs and water until smooth. In the third, combine the breadcrumbs, Italian seasoning, parmesan cheese, and a good pinch of salt.
Bread the chicken: Working with one cutlet at a time, using a fork, dredge it with flour, shaking off any excess. Dip it into the egg mixture, then press it into the breadcrumb mixture so it is well coated. Shake off any excess crumbs, then place the breaded chicken back on the baking sheet. Repeat with the remaining chicken pieces.
Cook: Set a large skillet (with sides) over medium heat and let it preheat. Add enough oil to cover the bottom by about ⅛ inch. To test the temperature, drop in a breadcrumb. It should sizzle right away.
When the oil is ready, add 2 chicken cutlets at a time, depending on the size of your pan. Cook for 2 to 3 minutes per side, or until golden brown and the internal temperature reaches 165°F. Transfer to a rack, sprinkle lightly with salt, and repeat with the remaining chicken (adding a little more oil to the pan as needed).
