In a bowl, combine the eggs and milk with a whisk. Set aside.
Place the bread crumbs on a plate. Set aside.
Place the cheese on half of the bread slices and add the anchovies and chili pepper. Close the sandwiches. Press lightly. Remove the crusts, if desired. Cut each sandwich into 2 rectangles.
Dip each sandwich into the egg mixture. Drain. Dredge in the bread crumbs and coat well.
In a large non-stick skillet over medium-high heat, fry 4 sandwiches at a time in half of the oil (¼ cup/60 ml), about 2 minutes on each side or until the cheese has melted. Repeat with the remaining sandwiches and oil (¼ cup/60 ml). Drain on paper towels.