Preheat your smoker to 225°F using your choice of hardwood pellets or wood chunks.
In a small bowl, combine the smoked paprika, garlic powder, onion powder, sea salt, black pepper, and dry mustard to create a dry rub.
Pat the pork ribs dry with paper towels and coat all sides thoroughly with the spice rub, pressing it into the meat.
Place the ribs directly on the smoker grates and cook for 3 to 4 hours until the meat is tender and begins to pull away from the bone.
While the ribs smoke, whisk together the tomato paste, 1 tablespoon of apple cider vinegar, coconut aminos, and liquid smoke in a small saucepan over low heat until smooth.
During the last 30 minutes of smoking, brush the prepared BBQ sauce generously over the ribs to create a tacky glaze.
In a medium bowl, toss the shredded cabbage and carrots with the remaining 1 tablespoon of apple cider vinegar and the olive oil.
Remove the ribs from the smoker, let them rest for 5 minutes, and serve alongside the chilled vinegar slaw.