Egg Pancake (Jidan Bing)

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1. 1Step 1: Mix the flour and warm water in a large bowl, adding water gradually, then knead into a smooth dough. Cover and rest for at least 30 minutes.
2. 2Step 2: Heat the oil in a small pan over low heat, add the cake flour and stir for about 1 minute until it smells cooked and no longer raw. Transfer to a separate bowl to cool.
3. 3Step 3: Divide the rested dough into 3 equal pieces. Roll one piece into a long strip about 4 inches wide, spread about a heaping teaspoon of the cooled flour-oil mixture over it, fold in half, then roll up like a cinnamon roll and stand it upright. Repeat with the remaining pieces.
4. 4Step 4: Cover the shaped dough with a damp cloth and rest for at least 5 minutes.
5. 5Step 5: Press each piece flat and roll it into a thin round pancake, about 1/8 inch thick, dusting with flour as needed.
6. 6Step 6: Beat one egg with chopped green onion and salt and pepper to taste until the yolk and white are fully combined. Repeat with the remaining eggs as needed, one per pancake.
7. 7Step 7: Heat a heavy-bottomed skillet over medium heat and coat with a thin film of oil. Lay one pancake in the pan and fry the first side for 30 to 60 seconds, until lightly set.
8. 8Step 8: Flip the pancake so it puffs. Pierce the top layer with a chopstick, pour the seasoned egg mixture over the surface, and spread it evenly.
9. 9Step 9: Cook until the egg is halfway set, then flip the pancake once more and cook until the second side is golden and crispy and the egg is fully set, with no runny egg remaining.
10. 10Step 10: Optional: for extra crispness when serving a group, keep the finished pancakes warm in a 350°F (180°C) oven for 5 minutes.
11. 11Step 11: Spread each pancake with sweet bean sauce or soybean paste, add chili paste if using, and top with a lettuce leaf. Fold like a taco and eat warm.