In a large soup pot, heat the oil over medium-high heat. Add the ginger, mushrooms and bean sprouts and cook, stirring, for 3 to 4 minutes. Add the broth, cover and bring to a boil.
In a large bowl, using a fork, combine the ground chicken with the egg yolks, bread crumbs, garlic, hoisin sauce, lime zest and pepper. Drizzle the chicken mixture with a little oil and roll about 1 tablespoon in your hands, forming a dumpling; repeat with the remaining mixture to make about 30 dumplings. Drop the dumplings into the simmering broth and cook thoroughly, about 10 minutes. Stir the cabbage and scallions into the mushroom broth and cook for 3 minutes. Serve the stoup in shallow bowls and top with pita chips.