In a mixing bowl, lightly beat egg yolk and pour in ice water, slightly mix. Add the flour all at once, stroke a few times with a fork just until ingredients are loosely combined. The batter should be somewhat lumpy.
In a small saucepan over low-medium heat, combine mirin, soy sauce and sugar. Cook for 3 to 5 minutes until sugar dissolves. Transfer to a bowl, add grated radish and ginger just before serving.
Heat about 2 inches of vegetable oil to 375 degrees F in a wok or deep-fryer. Flavor with sesame oil. Dry the vegetables well. Dust shrimp and vegetables in flour to soak up remaining moisture, shake off excess. Dip the shrimp and vegetables into the batter one by one. Drop 6 pieces at a time in hot oil. Do not overcrowd the pan. Fry until golden brown, turning once, about 3 minutes. To keep the oil clean, skim the small bits of batter that float in the oil between batches. Remove the fried pieces from the oil and drain on a paper towel for a few seconds. Serve with dipping sauce.