In a medium-sized bowl, beat together eggs, milk, and parsley; set aside.
Slice the mozzarella into 12 rounds. Make 6 sandwiches with the bread and mozzarella, dip each sandwich in egg mixture.
In a large skillet, lightly saute garlic in oil, then remove and discard garlic. Fry dipped sandwiches in the oil. When the sandwiches are browned, cut them into quarters on the diagonal and serve warm.