Scoop the rich cream that has risen to the top of the coconut milk into a bowl.
Cook and stir four spoons of coconut cream in a heavy saucepan over medium heat until the coconut oil begins to separate (some browning is okay).
Add lime leaves, fresh chilies (cut in half lengthways) and green curry paste to the coconut cream and cook until fragrant and well mixed (about one to two minutes).
Add chicken pieces and stir well to coat them with the paste.
Continue to cook to allow the flavors to penetrate the chicken but do not allow the paste to scorch.
Add coconut milk, the rest of the coconut cream, the fish sauce, the sugar and a pinch of salt.
Stir and bring the curry to a boil before reducing heat to a simmer and cooking uncovered for 15 minutes.
Cut vegetables into bite-sized pieces and start adding the ones which require the longest cooking, so that when you finish cooking the dish all the vegetables will be evenly cooked and look their best.
Correct the seasoning: Taste the sauce and add sugar, fish sauce, chilies or salt to suit your taste.
Stir in the whole basil leaves, garnish and serve.