Bring the chicken bone broth, water, minced ginger, and minced garlic to a gentle simmer in a medium pot over medium heat.
Add the chicken breast to the simmering liquid and cook for 12 to 15 minutes until the internal temperature reaches 165 degrees Fahrenheit.
While the chicken cooks, soft-boil the egg in a separate small pot of boiling water for 6.5 minutes, then immediately transfer to an ice bath.
Add the shelled edamame to the poaching liquid during the last 3 minutes of the chicken's cooking time.
Remove the chicken from the pot and slice it thinly against the grain.
Peel the cooled egg and slice it in half to reveal the jammy yolk.
Place the sliced chicken, edamame, and egg in a shallow bowl and pour over one cup of the poaching liquid.
Drizzle with tamari and toasted sesame oil, then season with sea salt and black pepper before serving.