The night before you plan to barbecue, cut pork shoulder lengthwise into two equal pieces (to speed up cooking), removing excess fat as needed. Combine seasoning-paste ingredients in a small bowl. Massage pork well with paste, then transfer to a large resealable plastic bag and refrigerate at least 8 hours.
About 45 minutes before you're ready to begin barbecuing, remove pork from refrigerator and let sit at room temperature (this will speed up cooking).
Combine mop-sauce ingredients with 1 cup water in a saucepan and warm up over low heat. Set aside 3/4 cup sauce to drizzle over meat just before serving.
Put wood chips in a bowl, cover with water, and soak at least 30 minutes.
To barbecue pork on a charcoal grill:
Prepare grill for barbecuing (see "Set Up Your Grill: Barbecuing," below). When temperature reaches 300°, lay meat on a cleaned and oiled cooking grate directly over drip pan and cover grill with lid.
Try to maintain a temperature between 250° and 300° throughout cooking (see "How to Control Your Heat," below).
After 1 hour, remove lid and, using a heatproof brush, baste meat all over with mop sauce. Add 10 to 15 briquets to fire (or more if coals have burned down significantly) and scatter an additional 1/3 cup drained soaked wood chips over coals. Check water level in drip pan; add more water as needed. Cover and keep smoking meat, maintaining grill temperature.
Repeat process (mopping meat, adding 10 to 15 briquets and 1/3 cup chips, checking water level) every hour, turning occasionally, until internal temperature of each pork piece reaches 190° and meat shreds easily, 1 1/2 hours per pound (3 to 5 hours total). If thermometer reads 190° but meat isn't tender, cook 30 minutes more.
Lift meat from grill and wrap in a double layer of heavy-duty foil, sealing tightly. Let meat steam at room temperature for about 30 minutes, then unwrap, reserving any juices that have accumulated in foil.
When meat is cool enough to handle, pull it apart into large pieces. Discard excess fat. Shred meat with your fingers or a pair of forks. Toss shredded meat with green onions and cilantro and drizzle with reserved juices and reserved mop sauce to taste. Serve pork with Chipotle Coleslaw and your choice of condiments.
To barbecue pork on a gas grill:
After preheating grill (see "Set Up Your Grill: Barbecuing," below), put meat on a cleaned and oiled cooking grate directly over drip pan. Follow instructions above for barbecuing on charcoal, starting with step 3 (ignore instructions about adding more charcoal and chips, but do add water as needed and dab and turn meat every hour). Adjust heat as needed to maintain an even temperature inside grill, preferably 250°, but you can go as high as 300°.
Note: Nutritional analysis is per serving.
Set up your grill: Barbecuing
ON CHARCOAL: Light 75 to 85 briquets in a chimney starter. Fill a drip pan (roughly 8 by 6 in.) to the brim with water and set in center of fuel grate. When coals are coated with ash, use tongs to arrange in a ring around drip pan. Set cooking grate in place. Cover grill and use a heatproof long-stemmed thermometer to take interior temperature through lid vent. Close grill vents as needed to bring temperature down to 300° (do not close vents all the way; the fire will go out). Scatter 2/3 cup drained soaked wood chips over coals just before adding meat.
ON GAS: If you have three or more burners, put drip pan in center under cooking grate, set grate over it, and turn outer burners to high. If you have two burners, put drip pan to one side and turn opposite burner to medium-high. Put 2 cups soaked wood chips in grill's smoker box or wrap chips loosely in foil, pierce in a dozen spots, and put directly on one of the hot burners. After about 20 minutes of preheating, reduce heat as needed to bring grill temperature to 300°.
How to Control Your Heat:
ON GAS: The beauty of a gas grill is ease of use: "You can operate it more like a cooktop, turning it down to reduce heat as needed," Cheryl Jamison says.
ON CHARCOAL: Once the briquets are burning, you can open the grill's vents to raise the heat, or close them to lower it (air feeds the fire). If you're grilling over a two-level fire, you can move the food around from hotter areas to cooler areas as needed. In fact, it's often a good idea to keep a small corner of your fuel grate free of coals, even when direct grilling. Invariably one steak or burger or sausage will cook faster than the others, and you'll want a small warming zone to stash it in while you finish the rest of the batch.