Season the veal well with salt and pepper. Dredge the cutlets first in the flour, then in the egg, and finally in the breadcrumbs. Preheat the oven to 350°F.

Add enough olive oil to a large skillet to come about 1/4-inch up the sides of the pan and heat over medium-high heat. Line a baking sheet with paper towels and place a wire rack on top.

When the oil is hot, fry the veal, in batches if necessary, until golden brown and crisp, 1 to 2 minutes. Transfer to the wire rack to drain while you cook any remaining veal. Toast the bread lightly in the oven, then remove the bread from the oven and increase the oven setting to broil.

Divide the veal cutlets evenly among the 4 bottom portions of toasted bread on a large baking sheet. Spoon the warm tomato sauce evenly over the veal, then top each sandwich with 1/2 cup of the mozzarella and 1/4 cup of the Parmesan cheese. Broil until the cheese is melted and lightly golden in spots. Remove from the oven and spread the top piece of bread with mayonnaise, if desired. Roughly tear or chop the basil leaves and scatter over the melted cheese. Place the sandwich tops over all and serve immediately.