Soak the wood chips in water for at least 30 minutes.
Fill a chimney starter to the rim with charcoal and burn the charcoal until it is lightly covered with ash. Separate the charcoal into two equal piles on opposite sides of the charcoal grate. Carefully place a large disposable foil pan between the two piles of charcoal and fill it about halfway with warm water. Let the coals burn down to low heat (250° to 350°F). Leave the lid off and all the vents open. If you're using a gas grill, prepare the grill for indirect cooking over low heat (250° to 350°F).
In a small bowl mix the rub ingredients. Coat the pork on all sides with the rub, massaging the spices into the meat. Allow the pork to stand at room temperature for 15 to 30 minutes before grilling.
In a food processor or blender, purée the tomatillos, canned green chiles, garlic, onion, oregano, and beer.
Related Grill Skills
Chopping an Onion
Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer's instructions, and close the lid. When the wood begins to smoke, place the pork in the center of the cooking grate, close the lid, and cook over indirect low heat for 30 minutes.
Remove the pork from the grill and immediately close the lid to maintain the temperature. Place the pork in a large disposable foil pan. Pour the tomatillo mixture around the pork and cover the pan tightly with foil. Cook the pork over indirectlowheat, with the lid closed, until the internal temperature of the meat reaches 190°F and the meat is so tender that it tears easily with a fork, 2 to 3 hours, depending on how steady the temperature is. To maintain the temperature, add 10 to 2 charcoal briquettes to each pile of charcoal every hour or so from the time you began to smoke the pork. Leave the grill lid off for about 5 minutes to help the ignite the charcoal.
When the pork is fully cooked, carefully remove the pan from the grill. Unwrap the pork (be careful of the steam) and transfer to a cutting board. Chop the pork into ½-inch chunks and shreds, discarding any large pieces of fat or tough pieces of meat. Pour the pan liquid into a large saucepan and spoon off most of the surface fat. Add the shredded meat and simmer the mixture uncovered for about 5 minutes to blend the flavors. Season with the cilantro, 1 teaspoon hot sauce, and salt and pepper to taste. The chile verde may be made up to this point one day ahead of serving and refrigerated overnight. Heat the chile verde before serving.
Serve the chile verde warm in bowls with rice. Pass the sour cream, limes wedges, and a bottle of hot sauce.