Pat both sides of slabs dry with paper towels. Using a sharp knife, remove thin membrane from back of each slab by slicing into it and pulling it off with a paper towel. (This will make ribs more tender and allow meat to absorb the rub better.) Combine salt, brown sugar, paprika, pepper, garlic powder, onion powder, dry mustard, chili powder, cumin, allspice, and herbes de Provence in a medium bowl. Rub 3/4 cup mixture evenly over both sides of slabs, and let stand at room temperature 30 minutes.
Prepare a charcoal fire in smoker according to manufacturer's instructions, substituting a mixture of 3/4 cup each of the vinegar and water in drip pan. Bring internal temperature to 250°F to 275°F, and maintain for 15 to 20 minutes. Place wood chunks on coals. Place slabs on smoker, meaty side up; cover with lid.
Smoke ribs, maintaining inside temperature between 250°F and 275°F, until meat is tender to the touch and pulls away from bones on the ends, 3 hours to 3 hours and 30 minutes. Remove ribs, and place on a baking sheet. Stir together remaining 1/4 cup each of vinegar and water. Spritz or brush vinegar-water mixture on both sides of ribs to thoroughly moisten. If desired, rub remaining 1/2 cup brown sugar mixture on both sides of ribs. Slice ribs between the bones, and serve.