Season your oxtail with the Traditional Oxtail Rub. Allow the meat to rest at room temperature while you prep the charcoal.
Fill a charcoal chimney up to the top with charcoal briquettes. Use your preferred method of lighting. I used a reasonable amount of lighter fluid poured down the center of the briquettes.
Light the charcoal briquettes. Let them heat until mostly white and very hot, about 20-25 minutes.
Place the oxtails on grill grates opposite from where you will put your heat source and very close to a vent.
Place three chunks of wood (apple, cherry or hickory) in a smoker box which will be placed on top of the coals.
Insert a probe thermometer into the thickest oxtail. Do so without penetrating all the way out of the bottom of the oxtail or touching the bone in the center of the oxtail. The oxtail you probe should be placed in the most evenly heated location on the grill grates. Avoid placing the probed oxtail in the hottest or coolest area of your grill/smoker.
Pour the entire charcoal chimney into the area opposite your oxtail and closest to a vent. Ensure that heated coals are very well situated to one side of the smoker/grill. Ensure that no oxtail is directly above the heated coals.
Place the smoker box with wood chunks directly on top of heated coals.
Open the vents on both sides of the smoker/grill as wide as possible. The external temperature in the grill/smoker should range from 390-400°F degrees. This mirrors the temperatures we would roast the oxtail to create browning in a traditional oven. The external temp in the oven is much less important than the internal temp of the oxtail and the browning that the high heat and smoke impart to the exterior of the oxtail.
Around the 25-30 minute mark, the first three wood chunks will have nearly burned out. Flip the probed oxtail on its side but leave it in its same area of the smoker/grill. Flip the remaining oxtail all the way over and then rotate the position of the oxtail closest to the heat source to an area furthest from the heat source.
Add the remaining three wood chunks to the smoker box directly on top of the coals and close the grill/smoker allowing the the oxtail to smoke for about 30 more minutes or until the probed oxtail reaches 190ºF internal.
When the oxtail are done smoking, they should appear reddish brown and slightly crispy on the outside.
Remove the oxtail from the smoker and place them in the cooking vessel of your pressure cooker with just enough water to completely submerge the oxtail.