Preheat oven to 350°. In a medium saucepan, simmer broth, ginger, and garlic, covered, 15 minutes to develop flavor.
Meanwhile, set duck on a baking sheet and bake until warm. Using a slotted spoon, remove ginger and garlic from broth and discard. Add noodles and soy sauce and let simmer until warmed through, about 5 minutes. Add bok choy and let cook just until wilted, about 2 minutes. Ladle soup into 4 bowls and drizzle each with 1/2 tsp. sesame oil. Set a few pieces of duck on top of each bowl of soup.
Note: Nutritional analysis is per serving.