Combine stock, garlic, ginger and chilli in a large pan; bring to the boil. Reduce heat to a simmer. Add chicken and cook, covered, 10 minutes, or until cooked through, turning once. Transfer the chicken to a plate, reserving the cooking liquid. When cool, slice the chicken fillets thinly.
Meanwhile, cook the soba in plenty of boiling water for about 4–6 minutes until al dente, or according to packet instructions. Add the beans and carrots for final minute of cooking time; drain and refresh under cool water.
Whisk the brown sugar, soy sauce, oil and reserved cooking liquid in a large bowl. Add chicken, noodles, beans, carrots and cabbage; mix thoroughly. Serve at room temperature.