EGGPLANT AND TOMATO SALAD

2 medium-size firm eggplants (about 1 1/4 pounds), rinsed
4 tablespoons extra-virgin olive oil
1/2 teaspoon salt, plus more to taste
3 cups ripe grape or small cherry tomatoes, rinsed
1/4 teaspoon freshly ground black pepper
1/4 cup red wine vinegar
12 small fresh basil leaves, or 2 tablespoons shredded large basil leaves
1/3 cup shredded fresh mozzarella or ricotta salata

Preheat the oven to 450 F. Trim the ends of the eggplant and slice cross-wise into 1-inch-thick rounds; cut each rounds into halves or quarters, to make roughly equal pieces no bigger than 2 inches on a side. Put the chunks on a baking sheet lined with parchment, or a silicone baking mat, and sprinkle a tablespoon of the oil and 1/4 teaspoon salt over them. Toss to distribute the oil , and spread the pieces apart so they’ll brown quickly.
Put the tomatoes on another parchment- lined sheet, sprinkle 1 tablespoon oil and a pinch of salt over them, roll them around, and spread them out. Put both sheets in the oven, and roast until both the eggplant and the tomatoes are soft, shriveled, and nicely caramelized on the edges, 30 minutes or more. While roasting, turn the eggplant chunks a couple of times, roll the tomatoes over, and shift the sheets around in the oven for even heating.
Let the vegetables cool on the sheets completely, then transfer them to a large mixing bowl. Toss gently with the remaining olive oil and salt, ground pepper, vinegar, and basil. Taste, and adjust the seasonings. Arrange the salad on a serving platter, or portion on salad plates, and sprinkle the shredded cheese on top.