For the shrimp: Lay the shrimp out in a single layer and dust both sides with the all-purpose flour.
Place a large, deep skillet or Dutch oven over medium-high to high heat and add about 2" of oil. Heat the oil to 375° F.
For the batter: When the oil is almost hot, make the batter. In a medium bowl, whisk together the egg and water. Then add corn starch, flour, and salt, and stir with fork. Do not overmix. It's ok if the batter is a bit lumpy. Then place a few ice cubes in the batter to keep it cold.
Dip individual shrimp into the batter to coat, and then carefully drop into the hot oil. Repeat with a few more shrimp. Do not overcrowd the skillet.
Fry until light golden color, about 2-3 minutes, and remove shrimp to a paper towel as they finish cooking.
For the sauce: In a small bowl, stir together all sauce ingredients.
Serve tempura shrimp while it's hot and crispy, with sauce for dipping.
