In a medium pot, combine rice, 1 ¾ cups water, 1 tablespoon of the olive oil, and ¼ teaspoon of the salt.
Bring to a boil over high heat, then cover and cook at a gentle simmer for 40 minutes or until water is absorbed. Cool slightly. (See note 1).
Meanwhile, preheat oven to 375°F with a rack in the middle.
On a large rimmed baking sheet, place the diced eggplant, onion, and garlic. Sprinkle with the remaining 2 tablespoons of olive oil, the remaining ½ teaspoon salt, and the pepper. Toss to coat evenly and spread in a single layer.
Roast for about 30 minutes, until tender.
Pour the rice, roasted eggplant mixture, olives, feta, basil, and chickpeas (if using) into a large bowl.
Sprinkle with the lemon juice and toss gently to combine.
Serve warm or at room temperature.