Put the pig feet in a pot with the stocks and bring to a boil. Skim and add the cinnamon, star anise, mushrooms, ginger, and soy sauce and pepper, to taste. Simmer, skimming every so often, until the pig feet are soft, about 3 hours. Strain. Taste and adjust seasonings; it may be salty from reducing so add a little water if needed. Let cool and refrigerate until it gels; it keeps for 3 days.
To make the vinegar reduction:
Combine the vinegars, the ginger and peppercorns in a large saucepan, bring to a boil, and cook until it's reduced to a glaze-like consistency. Strain through a sieve and refrigerate; it keeps indefinitely.
To make the foie mousse:
Preheat the oven to 275 degrees F.
Season the foie gras and scraps, if using, liberally with salt and pepper and let sit overnight in the refrigerator. Pack into a terrine mold, cover, and place the mold in a roasting pan filled with hot water. Bake until it just starts to melt and is warm in the center, about 45 minutes. Transfer the cooked foie gras to a food processor and run until smooth. Taste and adjust seasonings. Pass through a tamis or a fine-mesh sieve and repack into the terrine mold. Cover and refrigerate.
To make the dumplings:
Mix the flour and a pinch of salt in a large bowl. Add the boiling water and stir with a spoon until it comes together as a dough. Knead on a floured surface until smooth. Set in an oiled bowl, cover with plastic, and let rest 30 minutes.
In a small bowl, whisk together the egg, water, and a pinch of salt. On a floured surface, roll out the dough until it's a little less than 1/8-inch thick. Using a biscuit cutter or a knife, cut out 8 (3 1/2-inch) diameter rounds from the dough; try not to re-roll the scraps too many times.
Brush each wrapper with the eggwash. Cut a small square of foie mousse from the terrine and set it in the center of a wrapper, along with a few cubes of jicama and a small dollop of the gelled soup. Fold in half, press out the air pockets, and crease, pressing on the seam to seal and form half moons. Cook immediately, or freeze for up to 1 week.
Set up a steamer over a pot with 1-inch of boiling water. Steam the dumplings (if frozen, do not thaw first), without crowding the steamer, until puffed, 4 to 5 minutes.
While the dumplings cook, put the instant flour on a plate. Season the foie gras with salt and pepper and dredge in the flour. Heat a skillet over high heat, and when it's hot, sear the foie gras until browned on both sides but just warm inside, about 1 minute per side. Transfer to a board and cut into 8 pieces.
Decorate each plate with the vinegar reduction and arrange 1 dumpling on top. Top each dumpling with a piece of the seared foie gras and a pinch of the scallion julienne in the center. Serve with chopsticks and a Chinese soup spoon so that the diner can experience the juice in the dumpling.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.