Prepare the Chicken Cutlets: If using chicken breasts, slice them in half horizontally. Hold the chicken flat with one hand and slice smoothly with the other hand.
Season the Chicken: Generously season both sides of the chicken cutlets with salt and black pepper.
Set up a Dredging Station: Arrange three large plates or shallow bowls in a row. Place flour in the first bowl, beaten eggs in the second, and breadcrumbs mixed with Parmesan and Italian seasoning in the third. Set an empty plate or tray on the right for the breaded cutlets.
Bread the Chicken Cutlets: Working one at a time, coat each chicken cutlet in flour, then dip it in the beaten eggs, and finally coat it with the breadcrumb mixture. Press the breadcrumbs gently onto the cutlet to ensure they stick. Place the breaded cutlet on the reserved plate and repeat with the remaining cutlets. Let them sit for about 10 minutes to allow the breading to adhere.
Heat the Oil: Set a wire rack over a sheet pan next to your stove. In a nonstick skillet over medium-high heat, add enough oil to cover the skillet. Heat until it's shimmering but not smoking. Test the oil by dropping in a few breadcrumbs. If they sizzle gently, the oil is ready.
Pan Fry the Cutlets: Cook the cutlets in batches to avoid overcrowding the pan. Carefully add 1 or 2 cutlets into the pan, laying them down starting with one tip by the edge of the pan nearest you and laying them away from you towards the farthest edge of the pan to avoid splattering.
Flip: Cook until golden brown on both sides, about 3 minutes per side. Transfer the cooked cutlets to the wire rack to drain excess oil.
Serve: Optional: sprinkle flaky sea salt over the cutlets. Serve with lemon wedges for squeezing over the cutlets.