Cut the scallions into 3-inch lengths. Halve any thick white parts lengthwise so everything cooks at the same rate. Pat the scallions dry with a clean towel.
Stir the flour, cornstarch, baking powder, and salt together in a large bowl. Add the beaten egg and ice-cold water and whisk just until a thin, pourable batter forms. Do not overmix. Fold the scallions into the batter so every piece is lightly coated.
Stir all of the dipping sauce ingredients together in a small bowl and set aside until the sugar dissolves fully.
Heat a 10- to 12-inch skillet over medium-high heat. Add 1 1/2 tablespoons of the oil and swirl to coat the bottom.
When the oil shimmers, add half of the scallion batter to the pan. Spread the scallions into an even single layer and ladle loose batter over bare spots. Cook 3 to 4 minutes, until the bottom is deep golden and the edges look dry and crisp.
Flip the pancake, add a drizzle of oil around the edge, and cook 2 to 3 minutes more, pressing down gently, until the second side is golden and crisp.
Slide the pancake onto a board and repeat with the remaining batter and oil. Cut each pancake into wedges or squares and serve at once with the dipping sauce.