Place flour in a shallow bowl. Whisk eggs together in a separate shallow bowl. Combine bread crumbs and Parmesan in a third shallow bowl.
Sprinkle cutlets with salt and pepper. One at a time, dredge cutlets in flour, dip in egg and coat with bread crumb mixture.
Warm 1 Tbsp. oil and 1 Tbsp. butter in a large skillet over medium heat until butter is foaming. Cook half of cutlets, turning once, until browned on both sides and cooked through, about 5 minutes total. Transfer to platter and loosely cover with foil to keep warm; repeat process with remaining oil, butter and dredged cutlets. Serve immediately.