How to Make It
In a large, deep pot, combine the chicken, pork, ginger, scallions, carrot, broth and water and bring to a boil. Reduce the heat and simmer until the chicken is cooked through, about 30 minutes. Remove the chicken and, when it is cool enough to handle, pull the meat from the bones. Return the bones to the pot and simmer over moderately low heat until the broth is very flavorful and reduced to 6 cups, about 1 1/2 hours longer. Strain the stock and skim the fat from the surface. Reserve the chicken meat and pork for another use.
In a small bowl, combine the gelatin with 1/3 cup of cold water and let stand for 5 minutes. Whisk the softened gelatin into 3 cups of the hot stock until melted. (Reserve the remaining stock for another use.) Pour the gelatinized stock into a 2-quart glass or ceramic baking dish and refrigerate until firm, at least 3 hours or overnight.
In a medium bowl, stir 1/2 cup of the the all-purpose flour with 1/2 cup of the bread flour and 1/2 cup of boiling water until thoroughly combined. Turn the hot-water dough out onto a work surface and knead until fairly smooth, about 5 minutes.
In a glass measuring cup, combine 2 cups of room-temperature water with the saffron and let stand for 5 minutes. In the bowl of a standing electric mixer fitted with the dough hook, blend the remaining 4 cups of all-purpose flour and 1 cup of bread flour with the salt. Add the saffron water and beat at medium speed until a smooth dough forms, about 5 minutes. Add the hot-water dough and beat at medium speed until incorporated, about 5 minutes. Turn the dough out onto a work surface and knead it into a smooth ball. Wrap the dough in plastic and let stand at room temperature for 30 minutes or refrigerate overnight.
In a small bowl, cover the dried mushrooms with boiling water and soak until softened, about 20 minutes. Drain, squeezing out any excess liquid; discard the stems. Finely chop the caps and transfer them to the bowl of a standing electric mixer fitted with the paddle. Add the ground pork, crab paste, chives, potato starch, sesame oil, dark and mushroom soy sauces, sugar, ginger, salt and white pepper. Beat at medium speed until thoroughly combined, about 5 minutes.
In a food processor, pulse the jellied chicken stock until finely chopped; beat into the pork mixture at medium speed until the mixture is light and fluffy, about 5 minutes.
Cut the dough into 4 pieces. Working with one piece at a time and keeping the rest covered, roll the dough into a 1-inch-thick rope. Pinch or cut the rope into 3/4-inch pieces and roll them into balls. Then, using a small dowel, glass bottle or Chinese-style rolling pin, roll each piece of dough into a thin 3 1/2-inch round, dusting with flour as necessary. (For an alternative method, see Note.) Lightly dust the rounds with flour, transfer to a floured baking sheet and cover with a damp towel to keep them from drying out. Repeat with the remaining dough. You should have 4 dozen rounds.
Line 2 baking sheets with wax paper and dust lightly with flour. Working with 1 dough round at a time and keeping the rest covered, spoon a well-rounded tablespoon of the filling onto the center of the round. Using your fingers, pinch and pleat the dough around the filling, leaving a tiny steam vent at the top; transfer to the baking sheet and top with a goji berry, if using. Repeat with the remaining dough and filling.
Fill a pot with 2 inches of water and bring to a boil. Arrange the dumplings in a bamboo steamer basket in batches, leaving at least 1 inch between them. Cover and steam over the boiling water until the dough is shiny and the filling is soupy, about 5 minutes. Serve right away while you steam the remaining dumplings.
The jellied stock can be refrigerated in an airtight container for up to 3 days.
The dough can be tightly wrapped in plastic and refrigerated overnight.
The uncooked dumplings can be frozen on a baking sheet until solid and then transferred to a resealable plastic bag for up to 2 weeks.
Freeze uncooked dumplings on a baking sheet; seal in a plastic bad and freeze for up to 2 weeks. Steam until cooked, 10 minutes.
Crab paste (a concentrated crabmeat condiment) and mushroom soy sauce are available at Asian markets and online at amazon.com.
The vinegar dipping sauce alongside for dipping, or drizzle some of the sauce on top of each dumpling before eating.