Step 1 Make coconut-poached chicken: Combine coconut milk, chicken stock (or water), ginger and coriander roots and stems in a medium saucepan set over medium-high heat. Bring mixture to the boil, then reduce heat to a simmer and add chicken. (If chicken isn’t submerged, add enough water to just cover.) Simmer mixture gently for 15 minutes, or until chicken is just cooked. Remove saucepan from heat, leaving chicken in coconut broth for 5 more minutes.
Step 2 Transfer chicken to a work surface to cool; shred with a fork. Strain coconut broth and refrigerate.
Step 3 Meanwhile, combine fish sauce, brown sugar, lime juice (or lemon juice) and red chilli in a small bowl; stir to combine, until sugar dissolves.
Step 4 Combine carrots, bean sprouts, mint leaves, apples and half of the coriander leaves in a large salad bowl. Add shredded chicken to bowl. Pour dressing over chicken and toss lightly to combine. Scatter salad with peanuts and remaining coriander leaves, and serve.