Let brisket stand at room temperature 1 hour. Rub all over with 3 tablespoons of the rub and place fat-side up in a 13 1/2x9 1/2x3-inch disposable foil pan. Cover pan with foil.
Heat grill to medium-low (250 degrees F) and arrange for indirect cooking. Place brisket in the pan on grill rack away from the heat. Cover grill and cook 1 hour. Remove foil cover from the brisket and add smoker box or some of the wood chips to the grill. Cover grill and cook until brisket is tender, about 2 to 2 3/4 hours more or until meat is tender. If using a charcoal grill, add more wood chips about every 30 minute and add more coals as necessary.
Allow brisket to rest, covered, for 15 minutes before slicing. In a medium bowl, stir together Mop Sauce, ketchup, honey, Worcestershire sauce, and 1 1/2 teaspoons extra rub and serve with sliced brisket.
*Soak wood chips in enough water to cover for at least 1 hour before grilling.
Per Serving: cal. (kcal) 676, Fat, total (g) 39, chol. (mg) 159, sat. fat (g) 14, carb. (g) 31, Monosaturated fat (g) 17, Polyunsaturated fat (g) 2, fiber (g) 2, sugar (g) 26, pro. (g) 48, vit. A (IU) 1701, vit. C (mg) 8, Thiamin (mg) 0, Riboflavin (mg) 0, Niacin (mg) 9, Pyridoxine (Vit. B6) (mg) 1, Folate (µg) 16, Cobalamin (Vit. B12) (µg) 4, sodium (mg) 2443, Potassium (mg) 1018, calcium (mg) 71, iron (mg) 6, Percent Daily Values are based on a 2,000 calorie diet