Using a food processor, pulse-chop the giardiniera into a relish.
Pound the veal very thin (about 1/8 inch) and season with salt and pepper. Fill 3 separate shallow dishes with the flour, the eggs and the breadcrumbs seasoned with the nutmeg. Coat the veal with the flour, then the eggs, then the breadcrumbs.
Heat a layer of oil in a large skillet. Add the veal and cook over medium heat, turning once, until golden, 4 to 6 minutes. Drain on a rack.
Wipe out the pan; return to the heat. Add the butter and allow it to foam. Stir in the garlic for a minute. Add the parsley and lemon juice; remove from the heat.
Pile the roll bottoms with the giardiniera, lettuce, schnitzels, garlic butter and roll tops.