Place each veal cutlet between two sheets of heavy plastic and pound to 1/4-inch thickness. Season both sides with salt and pepper.
Set up a dredging station: flour in one shallow dish, beaten eggs in a second, and breadcrumbs (seasoned lightly with salt) in a third.
Coat each cutlet in flour, shaking off the excess. Dip in egg, then press into breadcrumbs to form an even crust.
In a large skillet over medium heat, melt butter with oil until it begins to foam.
Working in batches, pan-fry cutlets for 3–4 minutes per side, turning once, until they’re golden brown and crispy.
Transfer cooked schnitzel to a paper-towel-lined rack or plate. Keep warm in a low oven while frying remaining cutlets.
Serve immediately with fresh lemon wedges and a sprinkle of chopped parsley.