Combine the yogurt, mint, minced garlic, and salt in a small bowl. Cover and refrigerate until ready to serve—keeping this sauce cold is essential for the temperature contrast.

Microwave the spinach and water in a covered bowl until the spinach is wilted and reduced by half, 3 to 4 minutes. Let it stand, covered, for 1 minute. Transfer the spinach to a colander and press firmly with the back of a rubber spatula to release as much liquid as possible. Coarsely chop the spinach, return it to the colander, and press again to ensure it is dry.

Heat the olive oil and sliced garlic in a 10-inch skillet over medium-high heat. Stir constantly until the garlic turns light golden brown and is sizzling, 3 to 6 minutes. Stir in the coriander and turmeric and cook until fragrant, about 30 seconds.

Add the chickpeas, tomatoes, and the remaining water to the skillet. Reduce the heat to medium and cook, stirring occasionally, until the water has evaporated and the tomatoes have softened, 1 to 2 minutes.

Stir in the chopped spinach and salt. Cook until the spinach is uniformly wilted and glossy green, about 2 minutes. Transfer the mixture to a platter, drizzle with the remaining olive oil, and season with salt and pepper to taste. Serve hot with the chilled yogurt sauce.