1, In a bowl, combine the flour, 1½ teaspoons salt, the turmeric, cayenne, scallions, egg, soda water, and ice water and mix just until blended. The batter will be a little lumpy; do not overmix. The texture should be like slightly thin pancake batter. Add more ice water, 1 tablespoon at a time, if it is too thick.
2, Place the shrimp in a bowl, sprinkle with a pinch of salt and the black pepper, and toss to mix. Pour ½ cup of the batter over the shrimp and toss to coat. Add the sweet potatoes to the bowl holding the remaining batter and stir to mix evenly.
3, Pour the oil to a depth of ½ inch into a cast-iron frying pan or wok and heat over high heat to 350°F on a deep-frying thermometer. Line a rimmed baking sheet with paper towels, and place a large wire rack on a second baking sheet. Preheat the oven to 250°F.
4, When the oil is hot, place 5 battered sweet potato batons, side by side, in the oil, taking care to keep them close together. Place 4 or 5 more sweet potato batons on top, perpendicular to the first layer, creating a platform for the shrimp. Make 2 more sweet potato platforms alongside the first platform. Fry the sweet potato platforms for 1 minute, then top each platform with 1 battered shrimp. Spoon a small amount of hot oil over the shrimp to anchor them to the sweet potato batons.
5, Cook for 2 to 3 minutes more, until the sweet potatoes are golden brown on the first side. Using tongs or a slotted spoon, carefully turn each fritter and cook, shrimp side down, for 1 minute more, until the batter is just set on the second side. Using the tongs or slotted spoon, carefully transfer the fritters to the paper towel–lined baking sheet to drain briefly, then move them to the wire rack and slip them into the oven to keep warm. Repeat with remaining sweet potato batons and shrimp, always allowing the oil to return to temperature between batches.
6, Arrange the lettuce, mint, and perilla on a platter. Pour the fish sauce into small bowls for dipping. Transfer the fritters to a second platter and season lightly with salt. To eat, wrap a fritter in a lettuce leaf with the herb leaves and dip into the fish sauce.