Set up a gas grill for indirect low heat: Put a 9- by 13-in. drip pan on center burner (the indirect heat area) and fill it halfway with very hot water. Set cooking grates in place and heat the other burners to low (250° to 275°; these are the direct heat burners).
Meanwhile, on bony side of each rack of ribs, loosen membrane at one end with a table knife and pull off membrane with a paper towel. Set ribs on 2 rimmed baking sheets and coat all over with oil. Sprinkle generously all over with rub, patting it in. If you don't have a rib rack, scrunch 6 sheets of foil (1 1/2 ft. long) into logs 9 in. long and bend into arches about 3 1/2 in. tall.
Make 2 foil packs, each enclosing 2 fist-size chunks of applewood. Poke quarter-size holes all over each packet. Carefully lift each cooking grate in direct heat area and set packets directly on burners. Replace grates. Set ribs in rib rack over indirect heat running lengthwise to drip pan, or set ribs upright on cooking grate and wedge 3 rows of 2 foil arches between them to hold them in place.
Cover grill and smoke until meat has pulled about 1/2 in. from end of bones and a rack will bend easily, 2 1/2 to 3 1/2 hours; as meat cooks, add hot water to drip pan if needed to keep it about half full, and if some racks finish before others, remove and cover (see next step).
Transfer ribs to clean rimmed baking sheets and wrap snugly with foil. Stack pans, wrap snugly with a couple of layers of thick towels, and let meat rest 1 to 3 hours. (This makes it more tender. You can also wrap racks in foil and keep warm in a cooler lined with beach towels.)
Remove drip pan from grill. Reheat grill to medium-low (300° to 325°). Unwrap ribs. Brush one side of ribs with glaze and grill glazed side up, covered, about 3 minutes. Turn, brush with more glaze, and grill until ribs are browned and sizzling, 2 to 3 minutes total. Set ribs on boards, cut apart, and sprinkle with parsley.
* St. Louis-style ribs have been trimmed of the chewy lower skirt piece. Buy them at well-stocked grocery stores, or trim yourself: On the bony side, trim the flap of meat from the center, flush with the bones. Then cut the rack lengthwise between the 4- to 5-in.-wide rib section and the chewy skirt. Save scraps for soup.