In a bowl, mix the brown sugar, salt, garlic powder, cayenne, paprika, black pepper, cinnamon, cocoa, coriander and white pepper. Rub the mixture all over the brisket, set it in a baking dish and cover with foil. Refrigerate overnight.
Preheat the oven to 350°. In a large enameled cast-iron casserole, heat the oil. Add the brisket, fat side down, and brown well over moderately high heat, 6 minutes per side. Transfer to a plate.
Reduce the heat to moderate and add the onions. Stir well, cover and cook, stirring, until softened, about 15 minutes. Add the carrots, cover and cook, stirring, until the carrots begin to soften, 5 minutes. Transfer to a bowl.
Add the Coca-Cola, tomatoes and ketchup to the pot and stir over moderate heat. Add the brisket and any juices and spread the onions and carrots around the meat. If necessary, add enough water to half-submerge the brisket in liquid. Cover tightly and braise in the oven for 2 1/2 hours.
Transfer the brisket to a cutting board, cover with foil and let stand for 30 minutes. Raise the oven temperature to 425°. Slice the meat across the grain 1/4 inch thick, return to the casserole and spoon the sauce over the meat.
Return the pot to the oven and cook uncovered for 1 hour, or until the meat is fork-tender. Check every 20 minutes; if necessary, add water so the meat is half submerged. Remove from the oven and let stand for 15 minutes. Transfer the meat to a platter, spoon the onions, carrots and sauce over and serve.
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