1 large eggplant, sliced lengthwise 1/4-inch ( ½ cm) thick
1 teaspoon salt
3 tablespoons vegetable oil, divided
1 garlic clove, crushed
3 sprigs fresh thyme
2 sprigs fresh basil, divided
¼ cup white wine vinegar
1 red bell pepper, stem, seeds, and ribs removed then cut into 1/4-inch ( ½ cm) strips
1 medium tomato, sliced 1/2-inch (1 ¼ cm) thick then sliced cut in half crosswise
Place the eggplant slices in a single layer on a wire wrack and sprinkle both sides with the 1 teaspoon of salt. Allow to sit for 10 minutes then rinse with water and gently pat dry with paper towels.
Preheat the oven to 400ºF (200ºC).
Place the eggplant, oil, garlic, thyme, and one of the sprigs of basil on a baking sheet and gently toss to thoroughly combine. Arrange the eggplant in a single layer, then roast in the oven until the eggplant is tender, about 7 minutes. Transfer the baking sheet to the refrigerator to chill until the eggplant is thoroughly cooled, about 30 minutes.
While the eggplant is cooling, whisk together the remaining 2 tablespoons of oil, vinegar, and salt to taste in a small bowl. Remove the leaves from the remaining sprig of fresh basil.
When the eggplant is cooled, place each piece on a clean work surface. Place an even amount of red bell pepper strips in the middle, season with salt, and roll. With the seam side down, place a piece of tomato on each eggplant roll and top with a few fresh basil leaves. Secure the rolls with a toothpick and place on a platter. Drizzle the rolls with the vinegar mixture and serve.