Using a large mortar and pestle, grind together all the ingredients for the spice base until pasty. Set aside.
Heat the cooking oil in a wide thick-bottomed pan.
Spread the duck pieces in the hot oil and allow the undersides to brown.
Flip the duck pieces over and brown the opposite sides.
Stir up the duck and continue browning, with occasional stirring, until fat has been rendered.
Scoop up the duck pieces and set aside.
In the mixture of remaining oil and rendered fat, saute the spice base. Stir often until the solids separate from the fat.
Return the duck to the pan.
Pour in the coconut milk and broth.
Stir in about two tablespoons of fish sauce.
Bring to the boil, lower the heat, cover the pan and simmer the duck until the meat is tender and easily separated from the bone, about an hour and a half to two hours, depending on the age of the duck.
While the duck cooks, taste the broth occasionally and add more fish sauce, as needed.
When the duck is done, stir in the coconut cream.
Taste the sauce, add more fish sauce if needed, and allow the stew to come to a simmer.
Scoop out the duck pieces and transfer to a serving bowl, ladle the sauce over them and sprinkle with Thai basil and cilantro before serving.