Step 1

Whisk eggs in medium bowl to blend. Whisk in 1 1/2 cups cold water, 1/2 teaspoon salt, gochu garu, and 1/4 teaspoon black pepper. Add flour; whisk until smooth. Mix in shrimp, all onions, and carrot. Let batter stand 1 hour at room temperature.

Step 2

Whisk soy sauce, 2 tablespoons water, lemon juice, sesame oil, and gochu garu in medium bowl; divide among 4 to 6 small dipping bowls.

Step 3

Heat 1 tablespoon oil in each of two 10-inch-diameter nonstick skillets over medium heat. Add 1 cup pancake batter to each, spreading to edges of skillet. Cook until edges are firm and bottom is golden brown, about 4 minutes. Using spatula, turn pancakes over. Cook until second side is golden brown and shrimp is cooked through, about 4 more minutes (center will be soft). Increase heat to high and cook until bottom is deep brown, about 1 minute longer per side. Slide pancakes out onto cutting board. Repeat with remaining oil and batter, forming 2 more pancakes. Cut pancakes into wedges. Serve warm or at room temperature with dipping sauce.