To make the sauce for the tempura, combine dashi, soy sauce, mirin and sugar in a small saucepan and bring to a boil, stirring occasionally. Then lower the heat and let it simmer until sugar has completely dissolved, usually about 5 minutes. Remove from heat and set aside.
Prepare the shrimp by removing the shell, vein, legs and head, but keep the tail for decorative effect (please don't eat the tails).
In a deep fryer or pot, bring 3 cups or 1 1/2 inches of oil to 340 - 350F (170 - 180C).
While the oil is getting to temperature, make the tempura batter. Pour the flour into a medium bowl and set aside. In a separate bowl, whisk the egg into 3/4 cups very cold water, then slowly mix the egg mixture into the flour. Be careful not to over-mix the batter, and if needed, leave some lumps.
Dust corn starch over the shrimp, then coat the shrimp in the batter and drop in the fryer. Deep fry until golden brown, being careful to not add too many shrimp at once. You'll want to leave about a quarter of the oil surface clear to give them enough room.
Transfer to a wire rack to cool. Serve with the tempura sauce.
