Heat a grill pan over medium-high heat. Or, prepare a charcoal grill with hot coals or set a gas grill to medium-high heat.
Brush the eggplant slices generously with olive oil on both sides, sprinkle with salt and pepper and grill until charred on the outside and soft on the inside, 3 to 5 minutes on each side. Set aside and allow to cool slightly.
On a large rectangular platter, layer the tomatoes, mozzarella, eggplant and basil in diagonal rows. Drizzle generously with vinegar and olive oil and sprinkle with coarse sea salt. Serve at room temperature.