Set up a charcoal grill for indirect low heat (250° to 275°): Light 40 briquets in a chimney starter. Open grill's bottom vents fully. When coals are spotted with ash, about 20 minutes, put a 9- by 13-in. foil drip pan in middle of firegrate. Bank coals on either side of pan, piling them highest against walls of grill. Fill drip pan halfway with hot water. Let coals burn to low.
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.
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. Add 2 fist-size applewood chunks to each mound of coals.
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; whenever heat dips below 250°, add 5 to 7 lit briquets to each pile of coals (ignite in a chimney in a fireproof spot). If heat climbs over 300°, close vents, leaving at least 1 vent halfway open on lid and at bottom of smoker to keep fire going. As meat cooks, also add hot water to drip pan if needed to keep it about half full. 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°) and spread fire over firegrate. 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.