Preheat oven to 325 degrees. Rub beef with salt, pepper, ginger, and allspice. In a medium bowl, combine vinegar, tomato paste, brown sugar, onion, garlic, and 1/2 cup water.
Spoon half of the sauce into a 9-by-13-inch glass baking dish. Place brisket in dish, and spoon remaining sauce over the top. Cover tightly with heavy-duty aluminum foil (or a double layer of regular foil).
Bake until brisket is falling-apart tender, about 3 hours. Remove brisket from dish. Skim any fat from the surface of the sauce.
Transfer sauce to a medium saucepan; bring to a boil over high heat. Boil 5 minutes to reduce slightly. Slice brisket against the grain; serve with sauce.
If making the day before, prepare the recipe through step 3; slice the brisket, return it to the baking dish with the sauce, and refrigerate, covered with plastic. To serve, reheat brisket in its sauce in a 300-degree oven, skipping step 4.