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1
Combine the dashi, soy sauce and mirin in a saucepan. Bring to a gentle simmer and taste: the tsuyu must read noticeably saltier and more assertive than seems comfortable — it will be diluted by the tempura's oil and moisture over the course of the meal. Adjust seasoning accordingly and keep hot.
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2
Bring a large pot of unsalted water to a rolling boil. Cook the soba noodles according to the packet instruction, stirring to separate. Drain immediately and rinse under cold running water to halt cooking and remove surface starch. Divide among four bowls, then ladle the hot tsuyu over the noodles until the bowls are filled. The noodles should be fully submerged and the broth should steam visibly.
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3
Heat the frying oil to 180 °C. Prepare the batter immediately before frying: whisk the cold egg briefly into the ice-cold water, add the flour in one addition and stir only two or three times — lumps are correct, overworking activates gluten and destroys the crust. Toss the seafood and vegetables together, bind them loosely with batter, and lower gently into the oil as a loose patty. This step decides the dish: the kakiage must enter the oil colder and be fried slightly longer than standard — until the crust is distinctly firm and deeply set, not merely pale gold — because it will immediately begin to absorb broth at the table, and a crust that is only lightly set will collapse entirely before the diner has taken three bites. The exterior should be dry to the touch and audibly crisp when tapped.
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4
Lift the kakiage from the oil and drain briefly on a rack — not paper — so steam escapes from all sides and the crust does not soften from below. Place the kakiage on the rim of each bowl, or to one side of the noodles, so the diner controls the moment it enters the broth. Serve immediately; the progression from crisp crust to broth-soaked exterior is the intended experience and begins at the moment of service.
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5
Set shichimi togarashi on the table. The broth remaining after eating — enriched with tempura oil — should be offered as a final drink from the bowl.