Place chicken breasts into a large wide saucepan. Add chicken breast fillets and a good pinch of salt. Cover with cold water to cover by at least 3cm. Place over a medium high heat and bring gently to the boil. Once boiling, reduce heat to low and simmer for 10 minutes.
Turn heat off and cover the pan with a lid. Allow the chicken to continue cooking in the hot poaching liquid for a further 10 minutes. Remove chicken and transfer to a plate. Allow to cool at room temperature for around 20 minutes or until you are able to handle with your fingertips.
Once chicken is cool enough, using your hands, shred the chicken into rough bite size pieces. Cover and chill until required. (This can be prepared up to 2 days in advance)
Place the cabbages, carrots, spring/green onions, herbs and chilli in a large bowl. Add half of the chicken, peanuts, fried shallots and Nuoc Cham Dressing. Toss well combine. Transfer to a large plate or platter and top with remaining chicken, peanuts and fried shallots then drizzle with remaining Nuoc Cham Dressing. Serve immediately.