Stem, deseed, and cut the peppers into quarters crosswise. Soak the peppers in warm water for 30 minutes. Drain off the water and squeeze the peppers dry.
Put the peppers, ginger, garlic, ground coriander, cinnamon, turmeric, and shallot in a granite mortar or mini-chopper; grind until smooth.
Put the chicken in a mixing bowl along with half of the prepared paste, ½ cup of the coconut milk, and one teaspoon salt; mix well, cover, and chill 30 minutes up to overnight.
Make the basting liquid. Put the remaining curry paste in a one-quart pot along with the coconut or vegetable oil; set it over medium heat and fry until the paste become fragrant, about 2 minutes. Stir in the remaining 2 cups coconut milk, the remaining one teaspoon salt, sugar, and tamarind. Bring the sauce to a gentle boil and let it simmer about 3 minutes; remove from heat. Split the sauce into two equal portions. Use one portion to baste the chicken as it’s grilled; reserve the other portion to drizzle over the chicken once it’s done.
Thread the chicken onto the skewers (see post for instructions). Grill the chicken over moderate heat, basting it with one portion of the sauce. When the chicken is done, drizzle the reserved sauce over it and serve immediately.