Heat 3 tablespoons of the oil in a large frying pan over medium-high heat until shimmering.
Add the eggplant, arrange in a single layer, and season with salt and pepper. Cook undisturbed until the bottoms are golden brown, about 2 minutes. Stir the eggplant and continue to cook, stirring occasionally, until just tender, about 2 minutes more.
Remove to a medium bowl and set aside.Reduce the heat to medium, add the remaining 1 tablespoon oil to the pan, and heat until shimmering.
Add the onion, season with salt and pepper, and cook, stirring occasionally, until softened, about 5 to 6 minutes.
Add the raisins, vinegar, capers, and sugar and stir to combine. Cook until the vinegar has been absorbed, about 2 minutes.
Heat a grill pan or outdoor grill to medium high (about 375°F to 425°F).Meanwhile, arrange the bread slices in a single layer on a baking sheet. Using 1 tablespoon of the oil, very lightly brush the tops of the bread with the oil. Flip the slices over and brush with the remaining 1 tablespoon oil. Generously season one side only with salt and pepper.
Place the bread on the grill (reserve the baking sheet) and cook until grill marks appear and the bread is toasted and crisp, about 2 to 3 minutes per side.Return the grilled bread to the reserved baking sheet, seasoned-side up, and rub the seasoned sides with the garlic clove.To serve, divide the caponata mixture evenly among the bread slices.
Cut the bruschetta into pieces if desired before serving.