Whisk the egg and milk together. Peel a few thin strips from the parmesan with a peeler and grate the rest finely. Finely chop the parsley. Mix with grated parmesan, breadcrumbs, salt and pepper. Turn the meat first in the egg, then in the breading.
Fry the chicken fillets in 2 tablespoons of oil for 5 - 6 minutes on each side. Heat the rest of the oil. Halve the tomatoes, put them in the pan with the cut surface facing down and let simmer for 12 minutes.
Cut the lemon into slices. Turn the tomatoes 2 minutes before the end of the cooking time, season with salt and pepper, add the lemon and let it braise.
Serve with the meat. Sprinkle with the parmesan shavings.