Slice the pork belly into 1-inch by 8-inch strips. They should be about an inch longer than your buns.
In a small bowl, combine the spices. Rub all over the pork belly strips. Place on the Barrel House Cooker grill grate over a large platter or pan. Place in the refrigerator uncovered for 8-12 hours.
Heat the Barrel House Cooker according to manufacturer's instructions and set the vent to match your elevation. Place the grill grate in the top section of the barrel. Close the lid, and smoke at 250-275F degrees for 2 1/2 to 3 hours or until the temperature of the meat reaches about 200F degrees.
Open the bottom vent all the way. Lift the lid slightly and slide it to the side to allow air to flow through. This will heat the cooker up to about 400F degrees. Continue cooking the pork belly for 10 more minutes to get it nice and crispy.
Serve on a hot dog bun with ketchup, mustard and red pepper relish.
Whisk together the olive oil, vinegar, sugar, salt and pepper. Stir in the peppers, shallot and garlic.