Microwave 1 cup water and the bouillon cube in a microwave-safe glass measuring cup, 2 minutes. Stir in the soy sauce, mirin and sugar.
Heat 2 inches peanut oil in a heavy-bottomed pot until a deep-fry thermometer registers 380 degrees F. Meanwhile, whisk the flour, seltzer, eggs and 1/2 teaspoon salt in a medium bowl until almost smooth. Add 1 cup ice cubes and stir until they just begin to melt. Put the cornstarch in a shallow dish. Line a baking sheet with paper towels.
Working in batches, dredge one-third of the shrimp and vegetables in the cornstarch, then dip in the batter to coat, letting the excess drip off. Fry until crisp and lightly golden, turning once, 2 to 3 minutes. Remove with a slotted spoon and transfer to the prepared baking sheet to drain. Let the oil return to 380 degrees F, then repeat with the remaining shrimp and vegetables. Serve with the dipping sauce.
Photograph by Andrew Purcell