Heat 1 tablespoon oil in a small saucepan over medium heat. Add the diced onion and sweat until the onion starts to soften. Add the diced tomato, half the garlic, and a pinch of salt. When the sauce comes to a boil, reduce the heat and cook until thick. Season with salt and pepper. Set aside.
Preheat the broiler.
Trim the stems and leaves from the eggplants. Working from the center outward, cut each lengthwise into 5-mm thick slices. There should be 4 slices for each eggplant that are all about the same size.
Arrange the slices in a single layer on a baking sheet. Brush each side of each slice lightly with olive oil. Place the slices under the broiler until they start to brown, about 5 minutes. Turn the slices and brown the other side.