Bring the chicken stock, water, ginger, garlic and soy sauce to a simmer in a large pot over medium-high heat. Add the chicken and return to a simmer. Reduce heat to medium-low, and continue simmering until the chicken is tender and no longer pink on the inside, about 15 minutes.
Add the snow peas and carrot and simmer 5 minutes. Add the mushrooms, and continue simmering until the vegetables are tender, about 3 minutes. Stir in the spring onions, and serve.