Pork shoulder seasoned with a paprika-heavy dry rub, smoked and topped with a sweet tomato sauce.
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Trim the excess fat cap from the pork shoulder to 1/4 inch thickness and pat the meat completely dry with paper towels.
Combine paprika, brown sugar, salt, cayenne, garlic powder, and mustard to create the dry rub; apply heavily to all sides of the pork, pressing it into the meat.
Prepare your smoker for indirect cooking at a steady 225°F (107°C) using hickory wood for a deep, traditional Memphis flavor profile.
Place the pork in the smoker and cook until the internal temperature reaches 165°F, then wrap tightly in butcher paper to preserve the bark while tenderizing.
Continue smoking until the internal temperature reaches exactly 203°F, then remove and let the meat rest in an insulated cooler for at least 2 hours.
While the meat rests, simmer tomato paste, apple cider vinegar, molasses, and a pinch of the dry rub in a saucepan over low heat until thickened into a sweet glaze.
Hand-pull the pork into large succulent chunks rather than shredding it too finely, ensuring the exterior bark is distributed evenly throughout.
Toast the brioche buns lightly, pile the pork high, and finish with a generous drizzle of the warm sweet tomato sauce.
