Heat 2 teaspoons of the sesame oil in a medium pot over medium heat. Add the chicken and cook, breaking up with a wooden spoon into large clumps, until no longer pink, about 5 minutes. Add the ginger and jalapenos and cook until softened, about 3 minutes. Add the coleslaw mix and cook until lightly wilted, 2 minutes.
Add the broth and 4 cups water. Bring to a simmer over medium-high heat. Reduce the heat to medium and simmer to blend the flavors together, about 15 minutes.
Add the edamame and wonton wrappers (add the wonton wrappers a few slices at a time so they do not all clump together). Cook until the edamame are tender, 5 to 8 minutes. Remove from the heat and stir in the soy sauce. Divide among 4 bowls. Scatter the cilantro and scallions over the bowls and drizzle with the remaining 1 teaspoon sesame oil. Serve with additional soy sauce on the side for each person to season their own bowl of soup.
Per serving: Calories: 367; Total Fat: 16 grams; Saturated Fat: 4 grams; Protein: 32 grams; Total carbohydrates: 25 grams; Sugar: 1 gram; Fiber: 4 grams; Cholesterol: 100 milligrams; Sodium: 435 milligrams