If your butcher has not already done so, remove the thin papery membrane from the bone-side of the ribs by working the tip of a butter knife or a screwdriver underneath the membrane over a middle bone. Use paper towels to get a firm grip, then tear the membrane off.
Lay the ribs in a baking dish and pour the apple juice over them, turning to coat. (Use as much apple juice as you need to submerge the meaty side of the ribs.) Cover and refrigerate for 4 to 6 hours, or overnight.
Remove the ribs from the apple juice. Reserve the apple juice. Sprinkle the ribs on all sides with the Traeger Sweet Rub, rubbing it in with your fingertips.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 225F and preheat, lid closed, for 10 to 15 minutes.
Transfer the apple juice to a saucepan and place in a corner of the grill grate. (The juice will keep the cooking environment moist.)
Arrange the ribs, bone side down, directly on the grill grate. Cook for 4 to 5 hours, or until a skewer or paring knife inserted between the bones goes in easily.
Meanwhile, combine the barbecue sauce and brown sugar in a small saucepan. Generously brush the ribs on all sides with the barbecue sauce the last hour of cooking. If you like your ribs saucy, reapply the barbecue sauce just before serving.
Using a sharp knife, cut the slabs into individual ribs. Serve any remaining sauce on the side.