Preheat the oven to 200°F. Line a large baking sheet with paper towels. You will keep the pajeon warm in the oven on the baking sheet while you cook them in batches.
Make the dipping sauce: In a small bowl whisk together the soy sauce, vinegar, scallion whites, sesame oil, sugar, and sesame seeds. Whisk in the gochugaru if you would like a little heat. Set aside.
Make the batter: In a large bowl, whisk together the all-purpose flour, rice flour, salt, garlic powder, onion powder, and baking powder. Add 1 ½ cups water, egg, and sesame oil, and whisk until evenly combined. The batter should be thin and runny—add more water, 1 tablespoon at a time, as needed. Allow the batter to rest while you prepare the scallions.
Prepare scallions: Cut off and discard the root end of the scallions. Cut them in half crosswise, making 3- to 4-inch pieces. Cut the whites and any thicker green parts in half lengthwise. Separate the scallions into 4 even piles.
Cook the pajeon: Place a large nonstick pan over medium-high heat. Add 2 tablespoons oil and ¼ of the sliced scallions in a single layer into the pan. Pour about ½ cup of batter evenly over the scallions, making sure to fill the gaps. Cook for 3 to 4 minutes, until the underside is golden brown and crispy. Scoot a long thin spatula fully under the pajeon and flip. Cook the other side for 3 to 4 minutes, until browned. Transfer the pajeon onto the prepared baking sheet and keep warm in the oven while you make the remaining pajeon. Add a couple of teaspoons of oil to the pan before each new batch.
Serve the pajeon: Slice the pajeon into wedges or squares and serve with dipping sauce on the side. Cooked rice and kimchi are delicious accompaniments too!
Allow leftovers to fully cool and refrigerate wrapped in plastic wrap or in zip top bags for 3 to 4 days. To freeze, separate the pajeon with pieces of parchment paper and store in a freezer bag for up to 1 month. Defrost overnight in the refrigerator before reheating. To reheat, place in a nonstick pan over medium heat until warmed through.