Preheat the oven to 392 F (200 C). Cut the eggplant into small strips 4-6 cm long. Place on a baking sheet, and sprinkle with a little salt. Bake in the oven until soft and tender 20-25 minutes.
Prepare marinade by mixing all ingredients in a bowl. Finely chop the parsley, and press the garlic using a garlic press. Set aside.
Meanwhile, cut the onion into half rings, the bell pepper into thin strips, and grate the carrots.
Mix prepared vegetables, cooled eggplant, parsley with garlic, and sesame seeds. Stir in the marinade, and let it sit for at least two hours. Keep it in the glass jar in the fridge.
Notes
Eggplants absorb a lot of oil during cooking. That's why I don't add oil when I bake them. Moreover, we use enough olive oil in the marinade.