Make the Gelatin Soup Stock: Warm the chicken broth in a small saucepan until steaming (don't boil it). Sprinkle the gelatin over ¼ cup of the cold broth first and let it bloom for 5 minutes, then whisk it into the warm broth with the soy sauce, sesame oil, and salt. Pour into a shallow dish, cover, and refrigerate for at least 3 hours (or overnight) until firmly set. Dice into ¼-inch cubes — this jellied stock is what melts into hot soup inside the dumplings.
Make the Dumpling Dough: In a large bowl, stir the flour and salt together. Pour in the hot water while stirring with chopsticks until shaggy clumps form. Knead on a lightly floured surface for 8–10 minutes until the dough is smooth and soft (slightly tacky but not sticky). Cover with a damp towel and rest for 30 minutes — this relaxes the gluten so the wrappers roll out thin.
Mix the Chicken Filling: In a large bowl, combine the ground chicken, minced scallions, grated ginger, Shaoxing wine, soy sauce, sugar, salt, white pepper, and cold water. Stir vigorously in one direction for 3–4 minutes until the mixture becomes sticky and paste-like — this builds the texture that keeps the filling juicy. Fold in the gelatin stock cubes gently (don't crush them) and refrigerate the filling while you roll the wrappers.
Roll the Wrappers: Divide the rested dough into 4 portions, keeping the rest covered. Roll each portion into a log about 1 inch thick and cut into 6 pieces (24 total). Roll each piece into a thin 3½-inch round, keeping the edges slightly thinner than the center — this lets the pleats seal neatly while the base stays sturdy enough to hold the soup.
Fill and Pleat: Place about 1 heaping tablespoon of filling in the center of a wrapper. Pinch one edge up to form a first pleat, then work your way around, pleating and pinching the edges together — aim for 12–14 pleats — until you form a little purse shape. Twist the gathered top closed and pinch off any excess. Keep finished dumplings under a damp towel so they don't dry out.
Steam and Serve: Line a bamboo steamer with perforated parchment or cabbage leaves. Arrange dumplings 1 inch apart (they shouldn't touch). Steam over boiling water for 8–10 minutes until the wrappers turn slightly translucent. Serve immediately with a dipping sauce of black vinegar, soy sauce, and ginger matchsticks. To eat: place a dumpling on your spoon, bite a small hole to release the steam and sip the soup, then enjoy with a little vinegar.