Light a grill. Brush the bread on both sides with olive oil and grill over high heat until crisp on the outside but still soft inside, about 30 seconds per side. Transfer to a platter.
Brush the eggplant slices with olive oil and season generously with salt and pepper. Grill over moderate heat until charred on the bottom, about 5 minutes. Turn and grill until tender, about 3 minutes longer.
Top the eggplant with the tomato, mozzarella and basil. Cover the grill and cook until the cheese melts, 2 minutes. Transfer the eggplant to the bread, sprinkle with sea salt and serve.