Cut pork butt into 4-6 large chunks, leaving the bone in.
Season the chunks of pork generously on all sides with AlbuKirky Seasonings Green Chile Rub and refrigerate uncovered overnight. The next day, set up grill, smoker or Big Green Egg for an indirect cook. Add wood chunks or piece of wood for extra smoke flavor. Kirk uses Jealous Devil Charcoal and mesquite wood. Smoke the pork over indirect heat for 3-4 hours at approximately 275°.
While the pork smokes, prepare the braising liquid. Start by adding 1 quart of the chicken stock, 1 lb of the green chile, onion and garlic to a blender and blend until mostly smooth. This can also be blended in a tall pitcher with a stick blender (pictured). Add additional reserved green chile to increase the heat level to your preference and add additional reserved chicken stock as needed. Season mixture with 1-2 teaspoons of salt to taste. Be sure to taste test the braising liquid to ensure heat level and saltiness is as desired. Pulse to mix.
Remove the pork from the grill and place in a large dutch oven. Add the braising liquid to the pot until it is just even with the meat. This should take about 1/2 of the prepared braising liquid. Cover and place back on the grill at 300-350° or finish in the oven at 350° for 4-5 hours.
Check the pot every 20-30 minutes and add additional braising liquid as needed. Do not let the braising liquid boil off as this will cause the meat to dry out and become tough.
Pork is done when it shreds easily with a fork. Shred the meat in the pot allowing it to mix with the juices and chile.