Put the flour in a shallow dish. Lightly beat 2 eggs in another shallow dish. Mix the breadcrumbs and nutmeg in a third dish.
Pound the veal cutlets between sheets of plastic wrap to 1/8-inch thick. Sprinkle with salt and pepper. Dredge the veal in flour, then dip in the beaten eggs and coat with the breadcrumbs.
Heat a thin layer of oil in large skillet over medium-high heat. Cook the veal cutlets until deep golden, 2 to 3 minutes per side. Transfer to a rack to drain.
Wipe out the skillet and return to medium heat. Add 4 tablespoons butter and heat until the foam subsides. Add the capers and parsley and cook, stirring, 1 minute. Swirl in the lemon juice and remove from the heat.
Meanwhile, heat a pat of butter in another skillet over medium heat. Crack the remaining 4 eggs into the skillet and fry over easy.
Arrange the lettuce on the bottom halves of the rolls and top with the schnitzel. Drizzle with the caper butter, then top with the anchovies and fried eggs. Cover with the bun tops.