Place the flour, beaten egg and breadcrumbs in their own separate shallow bowl. Lightly salt and pepper the veal cutlets. Dip the cutlets into the flour followed by the egg and the breadcrumbs, shaking off any excess. With each step make sure the cutlet is evenly coated. Do not press the breadcrumbs into the meat and do not refrigerate or the coating will become soggy. Fry immediately.

Heat some oil in a small frying pan until about 330 degrees F (see Note). Once hot, add the cutlets and fry briefly on each side until lightly browned. Transfer to a plate and keep warm in the oven but do not tent with aluminum foil or the trapped steam will make the crust soggy.

Fry the onions in the same oil (first discarding excess oil as necessary) until lightly browned, 6-8 minutes. Add the bell peppers, the mushrooms, the garlic powder, onion powder, salt and pepper and fry until the peppers are crisp-tender, 4-5 minutes.

Divide the mixture in half in the pan and place the sliced cheese on top to melt.

Spread each side of the hoagie rolls with some mayonnaise and mustard. Place the fried cutlets on each roll and top with the vegetables. Serve immediately.