Preheat your smoker to 180-F as per the manufacturer's directions.
Rub the beef shank with cooking oil then sprinkle on salt and pepper. You want it well-seasoned.
Lay the shank on the smoker bone side down and smoke it at 180-F for about 4 hours.
Make the compound butter while the shank is smoking by pulsing the softened butter, garlic, chipotle peppers and adobo sauce, paprika, onion powder, and lime juice in a food processor until well mixed.
Remove the butter from food processor and wrap it in plastic. Refrigerate it for at least an hour or until it is hard.
Remove the shank from the smoker and get ready to wrap it in foil. You'll need heavy duty foil, or 2 layers of regular aluminum foil.
Slice about 2/3 of the compound butter and add it to the top of the shank before enclosing it in the foil.
Set the wrapped shank into an aluminum foil pan to catch any drips if you spring a leak in your foil. Don't worry if it doesn't fit - the bone end can stick out of the container.
Smoke at 300-F for an additional 5-6 hours or until the meat reaches 205-F with an internal thermometer.
Remove from the smoker and let it rest about 30 minutes (still wrapped) before serving.
Spoon the accumulated juices over the meat and you can also melt the rest of the chipotle butter to spoon over the top. Then serve!