Heat a large skillet over medium heat. Brush one side of each slice of sourdough with olive oil.
Place the meatloaf slices in the skillet and warm them for about 2 to 3 minutes per side, until heated through. Transfer them to a plate.
Place four slices of bread in the skillet, oiled side down. Layer each with a slice of warm meatloaf and some fresh mozzarella. Top with the remaining bread slices, oiled side up.
Toast the sandwiches for 2 to 3 minutes per side, turning carefully, until the bread is golden and the mozzarella begins to soften. Work in batches if needed.
Open each sandwich and add tomato slices and basil leaves. Season the tomato with salt and black pepper, then drizzle with balsamic glaze. Close the sandwiches, slice, and serve right away.