Step 1Prepare a charcoal grill for direct, medium-high-heat grilling or heat a gas grill to medium-high.
Step 2While the grill heats, mince the red onion by hand or cut the onion in 1-inch chunks and pulse in a food processor until minced and watery. Transfer to a medium bowl, and add the vinegar and 1 teaspoon each salt and pepper. Stir well, taste and season with more salt and pepper if you want, then let stand while you cook the rest of the dish.
Step 3Place the eggplants directly on the grill grate, cover and cook, turning occasionally, until charred on the outside and collapsed on the inside, 12 to 15 minutes. A paring knife should slide through the center easily when they’re ready.
Step 4Transfer the eggplants to a cutting board. Slice each in half lengthwise. Cut the tomatoes crosswise into ½-inch-thick slices. Arrange the eggplant and tomato slices on a serving platter, cut sides up, and season with salt and pepper. Spoon the pickled onions with their vinegar all over the eggplant and tomatoes. Serve warm or at room temperature.