Light 50 charcoal briquettes using a chimney. Run the wand of a thermometer through a cork and use the cork to plug one of the air vents in the grill lid. Leave the remaining lid vents open and adjust the lower vents as needed (if the fire gets too hot, close the vents; too cold, open them).
Combine the ingredients in a small saucepan and bring to a boil. Simmer over low heat for 10 minutes. Strain, cool and transfer to a spray bottle.
Mix the slather ingredients in a bowl. In another bowl, combine the rub ingredients.
Put the brisket on a large rimmed baking sheet and coat it with the slather. Sprinkle the rub all over the brisket.
When the coals are hot, push them to one side of the grill and set a drip pan half-filled with water on the other side. Using tongs, transfer 4 of the hot coals to the chimney to light an additional 25 briquettes. Set the brisket on the grill grate over the drip pan, fat side up, with the widest end facing the coals. Cover and cook for about 5 hours, maintaining a steady temperature inside the grill of 250° to 275° (add more lit coals, 25 at a time, every hour or so, as needed). Spray the brisket with the mop every hour.