1.Discard necks from chickens. Rinse chicken cavities; pat dry, inside and out, with absorbent paper. Using kitchen scissors, cut along each side of backbones; discard backbones. Turn chickens skin-side up; press down on breastbone to flatten. Using fork, prick skin several times. Rub each chicken with combined sugar, cumin and salt; stand 5 minutes.
2.Meanwhile, make nam jim. Blend or process ingredients until smooth.
3.Cook chickens on heated oiled covered barbecue, over low heat, about 35 minutes or until chickens are cooked through.
4.Meanwhile, place cucumber and herbs in a large bowl with 2 tablespoons of the nam jim; toss gently to combine.
5.Serve chickens with salad and remaining nam jim.
Coriander is one of the few fresh herbs to be sold with its root attached. It should be readily available from greengrocers. Nam jim is a generic term for a Thai dipping sauce; most versions include fish sauce and chillies, but the remaining ingredients are up to the cook’s discretion.