Step 1

Mix all spicy chili rub ingredients in small bowl, set aside.

Step 2

If using a fresh ham or picnic roast, remove skin (see illustration below). Massage dry rub into meat. Wrap tightly in double layer of plastic wrap; refrigerate for at least 3 hours. (For strong flavor, the roast can be refrigerated for up to 3 days.)

Step 3

At least 1 hour prior to cooking, remove roast from refrigerator, unwrap, and let it come to room temperature. Soak 4 (3-inch) wood chunks in cold water to cover for 1 hour and drain. Meanwhile, light a large chimney starter filled a bit less than halfway with charcoal briquettes (about 2 1/2 quarts, or about 40 briquettes), and burn until all the charcoal is covered with a layer of fine gray ash.

Step 4

Empty the coals into the grill; build a modified two-level fire by spreading the coals onto one side of the grill, piling them up in a mound 2 or 3 briquettes high, leaving the other half with no coals. Open the bottom vents completely. Place the soaked wood chunks on the coals. Position the cooking grate over the coals, cover the grill, and heat until hot, about 5 minutes (you can hold your hand 5 inches above the coals for 2 seconds). Use a grill brush to scrape the cooking grate clean.

Step 5

Set unwrapped roast in disposable pan (see illustration below) and place it on grate opposite the fire, (see illustrations below). Open grill lid vents three-quarters of the way and cover, turning lid so that vents are opposite chunks to draw smoke through the grill. Cook, adding about 8 briquettes every hour or so to maintain an average temperature of 275 degrees, for 3 hours.

Step 6

Adjust oven rack to middle position and preheat oven to 325 degrees. Place roast in pan and wrap with heavy-duty foil to cover completely. Place pan in oven and cook until meat is fork-tender, about 2 hours.

Step 7

Slide the foil-wrapped pan with the roast into a brown paper bag. Crimp top shut; rest roast 1 hour. Transfer roast to cutting board and unwrap. When cool enough to handle, "pull" pork by separating roast into muscle sections (see illustration, below), removing fat, if desired, and tearing meat into thin shreds with fingers. Place shredded meat in large bowl ; toss with 1 cup barbecue sauce, adding more to taste. Serve with remaining sauce passed separately.