Preheat a skillet or grill pan over medium heat.
Drizzle one side of each slice of sourdough bread with olive oil.
On the un-oiled side of one slice, layer the mozzarella cheese, tomato slices, and fresh basil leaves.
Drizzle the balsamic glaze over the toppings and season with salt and pepper.
Place the second slice of bread on top, oiled side facing out.
Carefully place the sandwich in the preheated skillet. Cook for about 3-4 minutes, or until the bread is golden brown.
Flip the sandwich and cook for an additional 3-4 minutes, until the other side is golden and the cheese is melted.
Remove from the skillet, slice in half, and serve immediately.