Using a mortar and pestle (or a mini food processor), grind all the ingredients for the curry paste.
Heat the cooking oil in a thick-bottomed pan.
Add the curry paste and saute (medium heat, of course), stirring often, until the solids start to separate from the oil.
Pour in the coconut cream and heat until bubbly.
Dump the chicken into the pan and stir to coat each piece with the curry sauce.
Stir in the palm sugar, a tablespoon of fish sauce and the cinnamon stick.
Mix the coconut milk with the chicken broth and pour into the pan.
When the sauce boils, set the heat to low, cover the pan and cook the chicken in the sauce for 30 to 40 minutes with occasional stirring, depending on how large the chicken pieces are.
Twice or thrice during cooking, taste the sauce and add more fish sauce, as needed.
Serve your Thai chicken curry topped with cilantro leaves with lime slices or wedges on the side.