Slice the tomatoes into quarter-inch rounds. Prepare two bowls, beat the eggs lightly in one bowl and mix the cheese, breadcrumbs and salt and pepper to taste in the other.
In a large frying pan, heat the oil to medium-high. When the oil has reached the appropriate temperature, reduce the heat to medium low. Next, quickly dip each tomato slice into the egg being sure to dip both sides completely then transfer into the breadcrumbs and cheese bowl.
Place the slices into the hot oil being careful to adjust the heat if the oil splatters. Fry each slice until browned and crispy before flipping, about 3-4 minutes. Be sure to monitor the tomato slices so they don't burn.
Once perfectly crispy and browned, remove the tomato slices from the oil and place on a paper towel lined plate. Arrange on a platter, topped with sliced fresh mozzarella, chopped fresh basil and drizzled with balsamic glaze.