To assemble the wontons, place wrappers on a work surface. Spoon 1 tablespoon of the shrimp mixture into the center of each wrapper. Using your finger, rub the edges of the wrappers with water. Fold the dough over the filling to create a half-moon shape, pinching the edges to seal; set aside. Heat 1 tablespoon sesame oil in a large stockpot or Dutch oven over medium heat. Add garlic and ginger, and cook, stirring frequently, until fragrant, about 1-2 minutes. Whisk in chicken broth, mushrooms and 2 cups water. Bring to a boil; reduce heat and simmer until mushrooms have softened, about 10 minutes. Stir in Bok choy and green onions. Stir in miso paste until well combined, about 1-2 minutes. Stir in wontons until cooked through, about 2 minutes. Serve immediately.