In a medium saucepan with a tight-fitting lid, combine the rice, 1½ cups water, and ½ teaspoon salt and bring to a boil. Stir the rice once, cover, and reduce heat to low. Simmer for 18 minutes. Remove from heat and let stand, covered, for 5 minutes.
Meanwhile, heat the oil in a saucepan over medium-high heat. Add the onion and cook, stirring occasionally, until softened, 4 to 6 minutes.
Stir in the tomatoes, eggplant, curry powder, 1 teaspoon salt, and ¼ teaspoon black pepper. Cook, stirring, until fragrant, about 2 minutes.
Add 2 cups water and bring to a boil. Reduce heat and simmer, partially covered, until eggplant is tender, 12 to 15 minutes.
Stir in the chickpeas and cook just until heated through, about 3 minutes.
Remove the vegetables from heat and stir in the basil. Fluff the rice with a fork. Serve the vegetables over the rice with yogurt, if using. Serves 4, with 339 calories and a healthy 9 grams of protein per serving.