This is an easy dish that makes use of all parts of the bird. It takes just over an hour to make from start to finish. While the chicken is cooking, make a side dish of vegetables, as well as some steamed rice, to soak up the delicious sauce.
Cut off the head, neck and wingtips from the chicken, and pull out the excess fat from the cavity of the bird. Cut the chicken into nine pieces: two wings (drumette and middle joint together), drumsticks, thighs and breast halves (cut the breast meat from the bones), plus the lower back. Put the upper back, wingtips, breastbone, head and neck into a saucepan and add about 600ml (2½ cups) of water. Bring to a boil then lower the heat and simmer for about 30 minutes. Strain out and discard the solids, reserving the liquid.
While the chicken stock is simmering, dry the chicken pieces with paper towels, then put them skin side-down on a cutting board and sprinkle lightly with salt. Turn the pieces over and sprinkle the skin side with salt, then leave at room temperature for about 30 minutes while preparing the other ingredients.
Finely chop the onion and thinly slice the garlic. Lay the lemongrass stalks on the cutting board and crush them along the entire length with a meat mallet or the side of a cleaver. Very finely chop the lemongrass. Cut the bird’s-eye chillies into thin rounds, shaking out and discarding as many seeds as possible. Slice the red and green banana chillies on the diagonal about 5mm (¼in) thick.
Take the chicken fat (from the cavity of the bird) and put it in a large skillet placed over a medium flame. Heat it until enough of the fat renders out to lightly coat the skillet. Remove and discard the solid part of the fat.
Turn the flame to high and, when the skillet is hot, add the chicken pieces skin side-down in one layer. Do this in batches, if necessary. Brown the chicken pieces then turn them over and brown the other side. Place the chicken pieces on a tray or plate.
Pour off all but about 20ml (4tsp) of fat from the skillet (if there's not enough fat, add some oil). Add the onion, garlic and a sprinkling of salt. Cook over a low flame until the onion is soft and translucent, stirring occasionally. Add the turmeric and chilli powder and stir constantly for about 30 seconds, then mix in the lemongrass, bird’s-eye chillies, banana chillies and the lime leaves.
Pour 300ml (1¼cups) of the chicken stock into the skillet and turn the flame to high. When the stock simmers, add the thighs, drumstick, wings and back, placing them skin side-down and nestling in the pieces so they are in one layer. Cover the skillet with a lid and adjust the heat so the liquid is at a low simmer. Cook for 10 minutes then turn the pieces over. Add the chicken breasts, laying them on top of the other pieces if they don’t fit in one layer in the skillet. Cover with the lid again and continue to simmer for about 10 more minutes, or until the chicken pieces are cooked.
Drizzle the coconut milk into the skillet, tilting and swirling the pan so the milk gets mixed into the liquid (if needed, take out some of the chicken pieces, to make this process easier). Taste the sauce and add more salt, if needed. If you took out the chicken pieces, place them back into the skillet and simmer for a minute or two, occasionally spooning the sauce over the meat. The sauce should lightly coat the chicken pieces; if it’s too thick, add more chicken stock.
For a casual meal, serve the chicken straight out of the skillet; for something a little more elegant, arrange the pieces on a serving platter. Scatter the toasted coconut and fried shallots over the chicken and serve with steamed rice and green vegetables.