Rinse meat and pat dry. Trim off all but a 1/2-inch fat cap, but don't remove fat layer between the flat and the point of brisket. Slice off any tough, thin membrane, called silverskin, from meaty side. Apply Texas BBQ Dry Rub all over brisket, coating meat evenly. Let it sit out for 1 hour to come to room temperature before cooking.
If you're using a charcoal grill, start with a chimney half full of charcoal and light chimney. When charcoal is ready, dump it into grill. Adjust vents on bottom of grill so half are open and half are closed and the lid vents are open. Set the grate in place and cover grill with lid. Continue to burn charcoal in a pile until embers are red-hot with a white ash. Add about 1/2 cup of the wood chips to fire and wait about 5 minutes, until smoke escaping through vents is white. Put brisket on grill and close lid.
If you're using a gas grill, preheat it with lid closed until temperature reaches 225°, then turn off heat on one side. Wrap 2 cups of the wood chips in an aluminum foil packet, poke holes in foil, and put wood chips on hot side of grill. Make 4 to 5 more packets to add during cooking time. Cover grill with lid for 5 to 10 minutes, until you see white smoke escaping from vents. Open lid and put brisket on side of grill that is turned off. Close lid.
Smoke brisket for 2 hours. If you are using a charcoal grill, add a handful of charcoal and a handful of wood chips to fire every 30 to 40 minutes. When smoke is no longer escaping through vents, add more chips to fire. If using a gas grill, add a fresh packet of wood chips to fire when white smoke is no longer escaping from vents.
After 2 hours, open lid and use a barbecue mop or a large basting brush to apply BBQ Mop Sauce on all sides of brisket. Rotate brisket 180 degrees and close lid.
Smoke brisket for an additional 2 1/2 hours, or until it registers 150° on an instant-read thermometer. (For best results, insert thermometer in a few places, aiming for thickest part of meat and avoiding fat.)
Remove brisket from grill and place on a large square of doubled heavy-duty aluminum foil. Baste generously with mop sauce and close foil tightly over brisket. (Keep wrapped for remainder of cooking time.) Return brisket to grill, close lid and smoke another 3 to 4 hours, continuing to add charcoal if necessary, until internal temperature registers 190°. Another way to check that brisket is ready is when the thermometer stem slides in and out of the meat without resistance; it should feel like a knife going through butter.
Alternately, after wrapping in foil, transfer brisket to a 225° oven to finish cooking. It won't lose any of its smoky flavor—all you're doing is continuing to cook the meat.
Line a cooler with a towel. Leaving thermometer in place, put wrapped brisket in cooler on top of towel. Fold towel over brisket and close cooler. Let meat rest in cooler 1 to 3 hours, or until you are ready to eat.
To serve, unwrap brisket and place on a cutting board. Run a knife between the flat and the point to separate the two brisket muscles. Trim excess fat from each muscle and slice each against the grain—it should be about the thickness of a pinkie finger. The meat should hold together, not fall apart or crumble. If the first slice falls apart, cut thicker slices. Pile brisket on a platter and serve with Spicy Texas BBQ Sauce on the side.
Combine kosher salt, unrefined evaporated cane sugar, packed light or dark brown sugar, chili powder, Mexican chili powder, chipotle chile powder, freshly ground black pepper, ground cumin, smoked sweet paprika, onion powder, garlic powder, celery salt, dry mustard and cayenne pepper in a bowl and stir. Store in an airtight container in a dry place for up to 2 months.
Combine beer, vinegar, oil, Worcestershire, chiles, peppercorns, garlic, thyme, bay leaf and 1/2 cup water in a saucepan over low heat. Add Texas BBQ Dry Rub and stir to combine. Cook over low heat about 5 minutes to bring flavors together.
Heat oven to 375°. Put onion, tomatoes and garlic on a baking sheet. Drizzle with 2 tbsp of the oil, season with pepper and salt, and toss to coat vegetables with seasoning. Spread vegetables in a single layer and roast at 375° for 30 minutes or until soft and browned in places.
Remove vegetables from oven and scrape them into a large saucepan. Add ketchup, cider vinegar, orange juice, brown sugar, white vinegar, Worcestershire, molasses, chili powder, paprika, coriander and cumin and whisk to combine. Bring to a boil over high heat. Reduce heat to low and simmer, uncovered, 2 hours or more, stirring occasionally, until liquid is thick enough to coat the back of a spoon. Let sauce cool to room temperature.
Pour sauce into a blender and puree, adding water if necessary to reach the consistency of barbecue sauce. Adjust seasoning to taste.