Combine stock, water, onion, garlic, ginger, star anise, black peppercorns, soy sauce and fish sauce in a large saucepan over medium-high heat. Cover and bring to the boil. Add chicken breast and simmer for 15-17 minutes or until chicken is cooked through. For the last 3 minutes of cooking, add bok choy.
Remove garlic, peppercorns, star anise and ginger and discard. Transfer chicken to a plate, and shred when cooled.
Prepare noodles according to packet instructions. Drain. Divide chicken, noodles, bok choy and stock between 4 bowls. Top each bowl with bean shoots, Vietnamese mint, coriander, spring onion, chilli and a lemon wedge.