Cut white portion of each green onion in half lengthwise; combine with green portions. Divide onion pieces into 4 even piles. Set aside.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, sugar, and salt in a medium bowl. Add ice water, stirring with a whisk until almost smooth.
Heat a large nonstick skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Arrange 2 onion piles, about 4 inches apart, in pan, keeping onion pieces parallel. Spoon a scant 1/4 cup batter over each onion pile, spreading gently into a circle that covers onions. Cook 3 minutes on each side or until crisp and golden. Repeat procedure with remaining oil, onion pieces, and batter. Serve immediately with Korean Dipping Sauce.