To prepare the shrimp filling, finely chop the scallions. In a bowl, combine the shrimp, salt, white pepper, sesame oil, and scallions, then mix until evenly combined.
To prepare the rice paper, in a bowl, beat the eggs. Place a sheet of rice paper on a clean working surface and lightly brush the beaten egg over both sides of the wrapper until it becomes flexible but not overly wet.
To assemble the dumplings, place about 1 tablespoon of shrimp filling near the bottom corner of the rice paper. Fold the bottom corner over the filling, fold in the sides, and roll tightly to form a dumpling. Repeat with the remaining wrappers and filling.
To pan-fry the dumplings, in a non-stick pan over medium heat, add the cooking oil. Carefully place the dumplings in the pan and cook for about 2 minutes per side, until golden and crispy and the shrimp filling is fully cooked through (145°F / 63°C).
To make the dipping sauce and serve, in a small bowl, combine the soy sauce, Chinkiang vinegar, and chili oil, then mix well. Serve the dumplings hot with the dipping sauce.