Heat the oil in a large saucepan over medium-high heat. Add the onion, garlic, and ginger and cook, stirring often, until softened, 5 to 7 minutes. Add the curry powder and cook, stirring, for 1 minute.
Add the chickpeas, spinach, 2 cups water, ¾ teaspoon salt, and ¼ teaspoon pepper to the saucepan. Bring to a simmer and cook, stirring occasionally, until the mixture is slightly thickened, 10 to 12 minutes.
Meanwhile, in a small bowl, stir together the yogurt, cucumber, cilantro, and ¼ teaspoon each salt and pepper. Serve the chickpea mixture with the yogurt sauce and naan.