While the meat rests, combine the ketchup, tomatoes, tomato paste, vinegar, mustard, granulated garlic, salt, pepper, brown sugar, and water in a large stockpot over medium heat. Simmer for 20 minutes, stirring, until the sauce thickens slightly. Whisk in the molasses last (it will burn if added too early) and blend with an immersion blender until smooth. Season to taste.
Move the rested BBQ beef brisket to a cutting board, fatty-side up with the wide, taller end to your left. The fully rested meat will have a distinct crust and will be tender and juicy inside. There should be a pink smoke ring beneath the crust. To carve, slice off the top or cap, which is full of most of the fatty, sinuous tissue, and reserve it for chopping. Now that the BBQ beef brisket is an even thickness, remove 2 1/2 inches from the left side, slicing at a 45° angle down and to the left. Next, remove 1 inch from the right side of the brisket in the same way. Reserve these 2 end pieces (often called the “burnt ends”) for chopping if you like. Burnt ends are fully charred and tasty, and many feel this is some of the best meat.
Slice the remaining center portion of the BBQ beef brisket into 1/4-inch-thick slices. Roughly chop the cap crosswise and lengthwise into 1/4- to 1/2-inch chunks. You can chop the 2 end portions with the cap, if you like.
Serve the sliced BBQ beef brisket immediately and pass the sauce on the side. If desired, serve the chopped meat immediately as well. [Editor's Note: The author prefers to save the chopped meat for later, when you can season it with some of the leftover coffee rub and a splash of barbecue sauce. We say dig in whenever you wish.]