Place a slice of mozzarella between two slices of bread to make a sandwich. Repeat with the remaining bread and cheese.
In a shallow bowl, whisk together the eggs, milk, salt, and pepper.
Place the flour in another shallow bowl, and the breadcrumbs in a third bowl.
Dip each sandwich first in the flour, ensuring all sides are coated, then in the egg mixture, and finally in the breadcrumbs.
Heat vegetable oil in a large skillet over medium heat. The oil should be about 1/2 inch deep.
Fry the sandwiches in the hot oil until golden brown on both sides, about 3-4 minutes per side.
Remove the sandwiches from the oil and drain on paper towels.
Serve hot, with a side of marinara sauce if desired.