Rub entire brisket with Stubb's Beef Rub. Let rest at least 30 minutes. This allows the rub to penetrate the meat.
While the brisket is resting, prepare the grill or smoker for indirect cooking at 225°F to 250°F (107°C to 121°C). If using charcoal, layer the soaked wood chips with the charcoal.
Grill 6 to 7 hours or until internal temperature of thickest part of beef reaches 180°F (82°C). (Gently move and turn brisket every 2 to 3 hours.) Carefully remove brisket from grill and wrap in foil. Return to grill, placing it back on unlit side. Cook 30 to 60 minutes longer or until internal temperature reaches 190°F (88°C). Remove brisket from grill or smoker. Let stand 30 minutes to 1 hour before unwrapping. Slice across the grain and serve with Stubb's Bar-B-Q Sauce on rolls, if desired.