Preheat a grill pan or skillet over medium heat.
Slice the ciabatta rolls in half horizontally.
Drizzle the cut sides of the rolls with olive oil.
Layer the mozzarella slices on the bottom half of each roll.
Add the tomato slices on top of the mozzarella.
Sprinkle salt and pepper over the tomatoes to taste.
Place fresh basil leaves on top of the tomatoes.
Drizzle balsamic glaze over the basil.
Close the sandwiches with the top halves of the rolls.
Place the sandwiches on the grill pan or skillet and press down gently with a spatula.
Grill for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from heat, slice in half, and serve immediately.