Preheat the oven to 210 degrees F (100 degrees C).

Sprinkle dry rub generously on all sides pork roast: place into a Dutch oven or heavy pot.

Divide liquid smoke between two 6-ounce ramekins; fill each with 1/2 cup water. Place ramekins in Dutch oven on either side of roast; cover.

Roast in the preheated oven until very tender, about 12 hours. Transfer roast onto a work surface (such as a cutting board); separate the meat from the bone using your fingers. Discard any large pieces of fat.

Roughly chop pork with a large knife or cleaver; drizzle with 3/4 cup barbecue sauce. Season with salt and black pepper.

Spread about 1 tablespoon barbecue sauce onto each bun; pile on pork to serve.