NOTES: You need a long-stemmed instant-read thermometer with a range from 200° to 400°. Clean old ash from the barbecue before starting. The herb spice rub and step 1 of the barbecue sauce can be made up to 2 days ahead. Cool, cover, and chill sauce. Store herb spice rub airtight.
4 cups (about 12 oz.) hickory or mesquite wood chips
In a bowl, pour water over chips to cover. Soak for at least 30 minutes.
Rinse meat and pat dry. Cut each rack of spareribs or back ribs, between ribs, into 2 or 3 pieces. Set aside 2 tablespoons herb spice rub. Rub remaining herb mixture on all sides of meat (rubber gloves help keep spices from sticking to your hands).
Ignite 55 charcoal briquets on firegrate of barbecue (see notes). When coals are coated with gray ash, in 15 to 20 minutes, mound against one side of firegrate. Set a drip pan (one fashioned out of heavy-duty foil is okay) in remaining space on firegrate. Add 3 briquets to mound; scatter 2 cups drained soaked wood chips over the top. Set grill in place. Lay meat on grill away from coals. Overlap ribs slightly, if necessary, to fit.
Cover barbecue and monitor temperature by inserting a long-stemmed instant-read thermometer through lid vent. Open or close vents to maintain a temperature between 225° and 275° (the temperature may start higher and take about 30 minutes to stabilize in that range); for more heat, open vents; for less heat, partially close vents. If temperature drops so low that you can't increase it by opening vents, add 1 or 2 more briquets and open all vents until they ignite.
After the first hour, remove lid; using tongs or thick hot pads, tilt grill to expose mound of coals; add 2 or 3 more briquets and 1 cup chips. If meat pieces overlap, adjust slightly so they smoke evenly. Replace grill and lid; continue smoking 1 hour longer, maintaining temperature between 225° and 275°. Repeat, adding 2 or 3 more briquets and remaining chips, and smoke another hour longer.
Lift meat from grill and wrap each piece in a double layer of heavy-duty foil, sealing tightly. Return meat to barbecue grill, not over coals. Add 3 to 5 more briquets, cover, and maintain temperature at 225° to 275°, adjusting vents as needed and adding 2 to 4 more briquets each hour. Cook wrapped pork spareribs or back ribs until meat pulls easily from bones, 2 to 3 hours for spareribs, about 1 hour for back ribs. Cook wrapped beef brisket until tender when pierced, 3 1/2 to 4 hours.
Set meat in a dish and open foil. Let rest in juices for 5 to 15 minutes, then lift from juices and transfer to a cutting board. Pour juices into a measuring cup. Spoon off fat, then add 1 cup juices to barbecue sauce; reserve remaining for another use.
Cut ribs apart between bones. Cut brisket across the grain into 1/4- to 1/2-inch-thick slices. (The smoke may have tinged meat pink near surface.) Add salt to taste. Serve with traditional barbecue sauce.
Per serving of spareribs: 479 cal., 68% (324 cal.) from fat; 35 g protein; 36 g fat (13 g sat.); 9 g carbo (0 g fiber); 329 mg sodium; 143 mg chol.
Per serving of pork back ribs: 550 cal., 72% (396 cal.) from fat; 36 g protein; 44 g fat (16 g sat.); 9 g carbo (0 g fiber); 367 mg sodium; 172 mg chol.
Per serving of brisket: 384 cal., 70% (270 cal.) from fat; 26 g protein; 30 g fat (12 g sat.); 1 g carbo (0 g fiber); 168 mg sodium; 99 mg chol.