Bring a saucepan 3/4 full of water to a boil, add the noodles and cook until just tender, about 5 minutes. Drain and set aside until needed.
In a large saucepan, heat the olive oil over medium heat. Add the onion and saute until soft and translucent, about 4 minutes. Add the ginger and carrot and saute for 1 minute. Add the garlic and saute for 30 seconds; don't let the garlic brown. Add the stock and soy sauce and bring to a boil. Add the chicken and edamame and return to a boil. Reduce the heat to medium-low and simmer until the chicken is cooked and the edamame are tender, about 4 minutes. Add the soba noodles and soy milk and cook until heated through; don't let boil.
Remove pan from the heat and stir in the cilantro. Ladle soup into warmed individual bowls and serve immediately.