In a bowl, whisk together the flour, egg, and ice-cold water until just combined. Be careful not to overmix – it's okay if there are lumps in the batter.

Heat the vegetable oil in a deep fryer or large pot to 350°F (180°C).

Dip the shrimp into the batter, allowing any excess to drip off, and carefully place them in the hot oil. Fry in batches for 2-3 minutes or until the shrimp are golden brown and crispy. Remove with a slotted spoon and drain on a paper towel-lined plate. Season with salt and pepper.

For the dipping sauce, combine the soy sauce, mirin, water, sugar, grated ginger, and chopped green onion in a small saucepan. Bring to a simmer over medium heat, then remove from heat and let cool.

Serve the Tempura shrimp hot with the Tempura dipping sauce on the side. Enjoy!