Step 1In a medium bowl, whisk together the kosher salt, celery salt, black pepper, onion powder, dried oregano, New Mexico chile powder, cumin, garlic powder, sweet paprika and brown sugar. This makes about 1 cup dry rub, more than you'll need for the ribs. Place the rub in an airtight container and store in a cool place away from direct sunlight; it will keep for about 2 months before the flavor starts to fade.
Step 2Peel the silverskin from the rib rack (the membrane on the underside of the rack). Rinse the rack under cold water, and pat dry with paper towels.
Step 3Drizzle a small handful of rub evenly over each side of the rack to give it a good coating; the surface of the ribs should be tacky, and the rub should adhere easily. Pat on the rub to make sure the ribs are entirely covered, and gently shake to remove any excess. Place the ribs on a rack on top of a rimmed baking sheet and refrigerate overnight.
Step 4The next day, prepare the smoker: Spread about 3 tablespoons wood chips in the center of the base of the smoker, directly over the burner. Place the drip pan (if using) over the chips, and a rack on top of the drip pan. Place the ribs in the center of the rack and cover with the lid, leaving the smoker open only a couple of inches. (Halve the rack if the whole rack won't fit, and smoke half at a time.)
Step 5Heat the smoker over medium heat just until you see smoke escaping through the opening. Close the smoker entirely and gently smoke for 1 hour. Depending on your stove, you may want to reduce the heat to medium-low so the ribs do not cook too quickly, or they will be tough.
Step 6Shortly before the ribs are done smoking, heat the oven to 250 degrees. In a measuring cup, combine the vinegar, water and Dijon mustard, along with 2 tablespoons of the rub and whisk together to form a "mop."
Step 7Place the smoked ribs in a baking dish and drizzle with the mop (pour over half the mop if smoking in two batches). Cover the ribs tightly with aluminum foil and bake until the meat is tender (you will know they're done when you bend the rack and the meat easily pulls away from the bone), about 1 hour more. For a crackly surface, uncover the baking dish and place the ribs under the broiler just until the surface crisps.
Step 8If smoking the rack in two batches: While the first half-rack bakes in the oven, smoke the second rack in the same manner as the first, using new wood chips (the first batch of wood chips should be reduced mostly to ash and can be washed down the sink; if they're too big, cool them completely before throwing away). Bake the second rack after smoking.
Step 9Serve the ribs warm.