Briefly wash the carp pieces and dry them well.
Season the eggs in a deep plate with salt and pepper and mix well. Put the breadcrumbs in a deep plate. Pull the carp pieces through the eggs, coat with the breadcrumbs on all sides. Set aside on a board for 30-40 minutes to allow the breading to firm up a bit.
Over medium heat, melt the fat in a large, heavy frying pan and fry the carp pieces until golden brown and crispy.
Remove, drain on paper towels and serve sprinkled with lemon wedges and finely chopped parsley.