1. To prepare pilaf, heat a large nonstick skillet over medium heat. Add 1 tablespoon oil; swirl to coat. Add 1 cup onion; cook for 6 minutes or until golden, stirring frequently. Add rice and the next 4 ingredients (through garlic); cook for 1 minute, stirring constantly. Add 1 2/3 cups water and bay leaf; bring to a boil. Cover, reduce heat, and simmer for 45 minutes. Let stand for 5 minutes. Discard cardamom, cinnamon, and bay leaf. Keep warm.
2. To prepare stew, heat a large Dutch oven over medium-high heat. Add 1 tablespoon oil, and swirl to coat. Add 2 cups onion; sauté for 6 minutes or until golden. Add ginger and the next 7 ingredients (through cinnamon stick); cook for 1 minute, stirring constantly. Add 2 1/2 cups water, carrot, 1/4 teaspoon salt, chickpeas, and tomatoes; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until carrots are tender and sauce is slightly thick. Discard cardamom and cinnamon stick.
3. Place 1 cup rice mixture into each of 4 bowls; spoon 1 1/4 cups chickpea mixture over rice. Top each serving with 2 tablespoons yogurt and 1 tablespoon cilantro.