Chill your liquids and dry ingredients: Measure the cold water and refrigerate it for 20–30 minutes. Chill the unopened carbonated water as well. Sift the cornstarch and all-purpose flour into a bowl, mix them together, and place that bowl in the fridge, too.
Prepare the Japanese sweet potato: Wash the skin, trim the ends, and slice the sweet potato into thin rounds, thick rounds, or sticks, whatever style you prefer. Make sure each piece still has a bit of skin. If using thick rounds, cut a shallow cross pattern on both sides. Soak the slices in cold water for 10 minutes to remove extra starch.
Preheat the frying oil: After your ingredients have chilled for about 20 minutes, heat the oil to 320°F.
Mix the tempura batter: In a small bowl, whisk together a few tablespoons of the chilled water and mayonnaise until the mayo loosens. Then pour in the remaining chilled water and cold carbonated water. Add the chilled flour mixture in a few small parts, gently mixing with chopsticks until just combined. Don’t whisk or over-mix; lumps are perfectly fine.
Test the oil: Drop a little batter into the oil. If it sizzles and floats to the top, it’s ready.
Coat the sweet potato: Pat each piece dry with paper towels, dust with a light layer of flour, then dip into the batter. Place each piece gently into the hot oil. Don’t overcrowd the pot.
Fry until golden and crisp: Fry for 5–6 minutes, flipping halfway, until golden and a skewer goes through easily. Keep the batter chilled between batches.
Drain and serve: Transfer the fried sweet potato tempura to a wire rack to let excess oil drip off. Serve hot and enjoy the perfect crispy tempura!