Preheat the smoker to 250°F. Add hickory, apple, cherry, or your favorite smoking wood.
Cut the skinless pork belly into approximately 1½-inch cubes and place them in a large bowl. Place them in a disposable aluminum pan.
Drizzle the pork belly with olive oil and toss to coat. Add the dry rub and toss again until the pieces are evenly seasoned on all sides.
Place the pan on the rack and smoke for 2½–3 hours, until the pork belly has developed a deep reddish-brown color and a flavorful bark.
Add the barbecue sauce and gently toss until the pieces are evenly coated.
Return the pan to the smoker, uncovered, and cook for another 1–2 hours, stirring once or twice, until the pork belly is very tender and the sauce is thick, sticky, and caramelized.
Check the larger pieces for doneness. A probe, skewer, or fork should slide into the meat with very little resistance. The internal temperature will typically be around 195–205°F, but tenderness is the best indicator of doneness.