Using kitchen scissors, cut along the back of the shrimp through the shell. Peel off the shell, leaving only the tail attached. Remove the vein, rinse the shrimp clean, and pat dry. Make 4 shallow cuts along the belly side. Flip the shrimp over and gently press along the back to straighten it.

In a bowl, whisk the egg with the cold water. Add the flour a little at a time, stirring gently. Add the salt and mix lightly. Do not overmix; the batter should remain slightly lumpy.

Heat oil to about 350°F (175°C). Dip each shrimp into the batter and carefully place into the oil. Fry until pale golden and crisp. Remove and drain.

In a pot, combine the water, soy sauce, mirin, sugar, dashi powder, and salt. Heat gently until just simmering. Do not let it boil.

Cook the soba according to the package instructions. Drain and rinse under cold running water to remove the starch, and drain well again.

Divide the noodles between two bowls and pour the hot broth over them. Top with kamaboko, green onions, and shrimp tempura.