Rinse the shrimp under cold water, pat dry, then cut each shrimp into about 3–4 small pieces and place in a mixing bowl.
Add the chives to the shrimp, then stir in the egg white, tapioca starch, chicken bouillon powder, salt, fish sauce, sesame oil, white pepper, sugar, and 1 teaspoon oil until evenly combined.
Cover the filling and refrigerate to marinate for 30 minutes.
Meanwhile, mix the soy sauce and Chinese black vinegar in a small bowl and set aside as the dipping sauce.
Place a wonton wrapper on a clean surface, moisten the four outer edges with a bit of water, add about 1 teaspoon of filling in the center, and fold the wrapper toward the middle to form a round dumpling; press edges to seal.
Repeat to fill all wrappers, keeping assembled wrappers covered so they do not dry out.
Heat a nonstick pan over medium–low heat and add enough oil to coat the bottom. Arrange dumplings in the pan, cover with a lid, and pan-fry until the bottom is golden brown, then flip and fry the other side until golden and cooked through, adding more oil if needed.
Serve the dumplings hot with the soy-black vinegar dipping sauce.