For the Tamarind paste:
Crack open the tamarind pod, removing the shells.
Add them to a large stockpot.
Add enough water to cover the pods.
Cover and bring to a boil.
Turn off the heat.
Let stand for an hour, or until the tamarind flesh is soft.
With your hands, remove the membranes and seeds from the tamarind.
Set aside until ready to use.
For the Chilis:
Toast the Guajillo and chile de arbol chilis on a griddle, turning frequently.
Do not let these burn. Only 1-2 minutes on each side.
With kitchen scissors, cut the top of the chili, then lengthwise, and remove the seeds and the membranes.
Repeat this step for every chili.
Add all the a large stockpot along with enough water to cover the chilis.
Cover and bring to a boil.
Turn stove off and let sit for 15 minutes, or until soft and pliable.
For the Tamarind Chili Sauce:
Add the tamarind paste, softened chilis, 1 cup chicken broth, brown sugar, onion, garlic, and salt in a blender.
Blend until smooth.
Taste for salt.
For the chicken:
Salt drumsticks.
Heat oil in a large pan.
Brown chicken drumsticks on all sides.
Remove from the pan and set aside.
Slowly add the Tamarind Chili Sauce and remaining chicken broth.
With a spatula, gently stir the sauce, scraping the bottom of the pan.
Return chicken to the pan.
Cover and bring to a boil.
Reduce heat and let simmer for 30 minutes, or until chicken is fully cooked.
Serve with rice.