Set the oven to 400F while you prepare the dish.
Place eggplant cubes in a large bowl. Sprinkle some salt over it in order to get the bitterness out. Leave it for 20 minutes at room temperature, then rinse with water and pat it dry with a cloth.
In a saucepan over the stove top, add 2 tbsp oil on medium heat. When it's hot, add onions, peppers, and carrot. Cook for 2-3 minutes, stirring every couple seconds so it doesn't burn.
Then add the garlic, bay leaf, and spices. Stir it for another 2 minutes, then add in eggplant, tomato, chickpeas, and chickpea water.
Keep stirring and let it boil on medium-high heat for 10 minutes. Remove from stove, and pour onto a baking sheet or a greased baking tray / baking dish, in a single layer.
Cook in the preheated oven for 45 minutes until the eggplant is soft. If you need more water, you can sprinkle in a few spoons at a time over top of the mixture.
Once it is baked, remove from the oven and drizzle the tablespoon of olive oil on top.
Serve warm with some yogurt, grains, and cilantro or fresh parsley!