- Line 2 large baking pans with paper towels. Sprinkle both sides of eggplant slices lightly with salt. Place eggplant on paper towels and let stand until salt draws out water, about 1 hour. Rinse off salt and pat sliced dry.
- Preheat broiler or grill. Brush eggplant slices with olive oil. Grill or broil until just golden on both sides and tender, turning once, about 8 minutes. Cool.
- Heat 2 tablespoons olive oil in heavy large skillet over medium heat. Add garlic and sauté until fragrant, about 1 minute. Add carrot and sauté until almost tender, about 2 minutes. Toss in zucchini, bell pepper and cumin and cook until vegetables are crisp-tender, about 5 minutes.
- Remove from heat and stir in tomato, cilantro and mint. Season to taste with salt and pepper. Cool.
- Place eggplant slices on work surface. Divide vegetable mixture among slices, placing vegetables at narrow end of eggplant slices. Roll up eggplant with colorful vegetables peaking out on each end.
- Transfer to platter, seam side down. Cover with plastic wrap and chill. (Can be prepared 1 day ahead.) Garnish platter with cilantro and mint and serve.