Sprinkle the chicken with the Jerk Rub, then saute or grill the chicken until firm but not cooked all the way, about 4 minutes per side.
Remove to strainer and let sit for 1/2 hour to drain off as much of the juice as you can. Add the chicken to a pot. Cover the chicken 1/4 of the way up with the Jerk Base and then fill the pot with Jerk BBQ Sauce to the 3/4 point of the chicken. Simmer until the chicken starts to fall apart, about 45 minutes.
Remove the chicken to a clean strainer to drain, reserve the liquid, put back into the pot and reduce the contents of the pot by 1/4. While the liquid is being reduced, use 2 forks to pull the chicken apart. After the liquid is reduced, add the chicken back to the pot. It is ready to use at this point and can be made into sandwiches or served over rice.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.
Combine the sugar, onion powder, 5 tablespoons salt, 3 tablespoons black pepper, garlic powder, allspice, cayenne, nutmeg, thyme, orange peel, cinnamon, sage, ginger, jalapeno powder, habanero powder and lime peel in a bowl and stir to combine.
For the jerk base: Combine the yellow onions, green onions, jalapeno pepper, white sugar, brown sugar, cayenne, allspice, thyme, pepper, sage, nutmeg, cinnamon, vinegar, orange juice, soy sauce, rum, oil and lime juice and simmer for 1 1/2 hours. When the onions are very tender, remove from heat and allow to cool to room temperature. In batches, use a blender to puree until smooth.
For the jerk BBQ sauce: Combine 1/2 the Jerk Base recipe with the store-bought BBQ sauce and honey in a large bowl and stir to blend.