To make the shrimp filling, in a bowl, add the shrimp and season with salt and white pepper. In a pan over medium-high heat, add 1 tablespoon of cooking oil. Add the shrimp and cook until about halfway done, just until they begin to turn pink. Sprinkle in the chopped scallions and combine. Remove from heat and let cool slightly.
To soften the rice paper, in a bowl, crack the egg and whisk thoroughly. Lay one sheet of rice paper flat on a clean surface. Brush a thin, even layer of beaten egg on both sides of the rice paper. Wait about 20 seconds until it becomes flexible. If still stiff, brush on a little more egg.
To assemble the dumplings, place a portion of shrimp filling along the bottom corner of the softened rice paper. Roll into a log shape, then gently twist both ends to form a spiral-like dumpling. Repeat with the remaining filling and wrappers.
To pan-fry the dumplings, in a pan over medium heat, add the cooking oil. Place the dumplings in a single layer and cook for about 2 minutes per side until golden and crispy. Remove and drain briefly.
To make the dipping sauce, in a small bowl, whisk together the soy sauce, Chinkiang vinegar, and chili oil. Serve the dumplings hot with the dipping sauce.