For the beef brisket: Take the brisket out of the refrigerator 1 hour before you want to put it on the smoker.
While the meat is resting, add charcoal to the firebox of the smoker to provide indirect heat. Light the charcoal and let burn. When the charcoal begins to ash over, add your mesquite wood.
For the splash: Pour the vinegar, barbecue sauce, ketchup, Worcestershire, olive oil, mustard, paprika, salt, pepper and hot sauce into a large glass measuring cup and mix well. Use a funnel to pour the mixture into a clean empty whiskey bottle. Set aside.
For the spice rub: In a medium bowl, combine the chile powder, paprika, cayenne, garlic powder, onion powder, salt, black pepper, brown sugar and mustard and mix together. Rub the brisket with the spice rub all over. Place the brisket fat-side up in the smoker. The fat will render while cooking; it basically melts and releases oils into the brisket to help keep it moist while cooking.
Maintain a cooking temperature inside the smoker of 200 to 225 degrees F, adding coals and wood every 2 hours or as necessary. Use the splash on the brisket every time you add new coals. When pouring the splash onto the brisket, cover half of the bottle opening with your thumb and shake directly onto the brisket. Try not to lift the lid of the smoker at any other time. Rule of thumb for cooking time is 1 1/2 hours per pound. However, there are many variables, including how many times you open the lid or how steady you maintain the temperature of the smoker. The best way to judge if your brisket is ready is by checking the internal temperature of it with a meat thermometer.
Once the brisket reaches 170 degrees F, place in an aluminum roasting pan, add the rest of the splash and tightly wrap in aluminum foil. Place back in the smoker at 225 degrees F until the internal temperature reaches 190 degrees F, about another 2 hours. Let rest for 20 minutes, then unwrap and slice against the grain.
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