Butterfly the chicken breasts to create 4 thin cutlets. Gently pound them with a meat mallet until approximately 5mm thick and evenly flattened.
Mix the breadcrumbs, grated parmesan, 1 tbsp chopped parsley, salt, and black pepper on a wide plate.
Whisk the egg, milk, salt, and black pepper together in a shallow bowl.
Dip each chicken cutlet into the egg mixture, allow the excess to drip off, then coat thoroughly with the parmesan breadcrumb mixture. Gently shake off any loose coating.
Place the coated chicken on a clean plate and let it rest for approximately 5 minutes.
Heat enough neutral oil to generously cover the base of a large frying pan over medium-high heat. Fry the chicken for approximately 2–3 minutes per side until evenly golden, crispy, and completely cooked through.
Garnish with additional chopped parsley and serve with lemon wedges. Place the chicken over pasta tossed in tomato sauce, if desired.