Preheat the oven to 400°F.
For the eggplant spread, pierce the eggplant in several places with the tines of a fork. Wrap in aluminum foil and bake for 1 hour. Unwrap the eggplant, let cook slightly, and cut it in half. Scoop the cooked pulp onto a cutting board, discarding as many seeds as possible. Coarsely chop the eggplant and plant it in a mixing bowl. Add the basil leaves, lemon zest, oil, and raisins. Combine well. Season with salt and pepper. Set aside.
In another bowl, mix the chevre with 2 tablespoons of the oil and season to taste with salt and pepper.
Preheat the broiler.
Assemble the sandwiches. Divide the eggplant spread evenly atop the slices of toasted peasant bread. Cover evenly with the whole basil leaves. Spread the chevre mixture over the basil leaves and top each sandwich with a tomato slice. Brush the tomatoes with the remaining 1 tablespoon olive oil and sprinkle with salt and pepper.
Place the sandwiches on a baking sheet and broil 3 to 4 inches from the heat source until the tomato just starts to brown, 2-3 minutes. Sprinkle the tops with the slivered basil and serve immediately.