Heat the oven to 200 degrees while you prepare the three components of the breading. Sift flour into a shallow dish and whisk to combine with 1 teaspoon salt and the pepper. In another shallow dish, lightly beat eggs. In a third shallow dish, whisk to combine breadcrumbs and remaining teaspoon of salt. Dredge one cutlet at a time in the seasoned flour, turning to coat, and shaking off excess. Next dip in the eggs, again making sure to coat completely and to allow the excess to drip back into bowl. Then coat with breadcrumbs, patting firmly so they adhere but being careful not to coat too thickly. Place coated cutlets on piece of parchment paper or a large baking sheet.

Heat 1/4 inch of oil in a large skillet over medium heat until it is 350 degrees. Working in batches to avoid crowding pan, cook cutlets until golden brown on the bottom, 1 to 2 minutes. Flip with a flexible thin spatula and fry until the other side is golden brown and cutlets are cooked through, 1 to 2 minutes more, monitoring temperature of oil to maintain 350 degrees. Transfer to a baking sheet lined with a double layer of paper towels and keep warm in the oven.

Pour off and discard oil remaining in skillet, then wipe clean with paper towels. Working in batches again if necessary, melt the butter in the same skillet over medium heat until sizzling. Set pan-fried cutlets in the pan to coat one side with butter, then quickly flip to coat the other side.

Arrange the cutlets on a platter, sprinkle with chopped parsley and serve with lemon wedges.