For the tempura batter, whisk together the chickpea flour, water, salt, black pepper, and turmeric in a medium bowl. Add the eggplant and toss to coat. Add the ice to keep the batter cold and thin it out slightly as you heat up the oil.
Add about 1 ½ to 2 inches of oil to a medium saucepan with deep sides. Bring the oil temperature to 350F over medium-high heat.
Add half of the eggplant, allowing the excess batter to drip off each piece before adding it to the oil. Cook until the eggplant is tender and the batter is golden brown, about 5 minutes. Transfer the cooked eggplant to a paper towel-lined plate to drain the excess oil, and cook the remaining eggplant the same way.
For the sauce, whisk together all ingredients.
Serve the eggplant hot, with the sauce on the side for dipping.
Notes
Oil for Frying: Use an oil with a high smoke point, such as peanut oil or canola oil.