Preheat oven to 350°. Mix 1 tbsp. salt, pepper, mustard, and thyme together in a small bowl. Rub mixture all over brisket. Heat oil in an oval oven roaster (about 12 in. by 17 in.) or a wide 8-qt. pot* over medium-high heat. Add brisket and cook, turning once, until a dark brown crust forms, 4 to 5 minutes per side. Transfer brisket to a plate.
Add 2 cups broth to pot and bring to a boil, scraping any browned bits from bottom of pot. Stir in wine, prunes, and brown sugar. Return brisket to pot, fat side down, and cover with onions and garlic. Cover pot and put in oven. Cook for 3 hours, turning meat halfway through. Turn meat again and add remaining cup broth and carrots to pot. Cook, covered, until carrots are tender, 30 to 45 minutes. Let cool, then chill overnight (to firm meat).
Preheat oven to 350°. Skim fat from pan juices and discard it. Transfer brisket to a cutting board and slice across the grain. Fan out meat slices in a large roasting pan. Using a slotted spoon, arrange onions, carrots, and prunes over meat.
Boil juices remaining in pot over high heat about 10 minutes to reduce somewhat. Season to taste with salt and pepper. Pour 2 cups of juices over meat (save the rest for soup), cover roasting pan tightly with foil, and bake until meat is hot, about 45 minutes.
Transfer meat to a large platter, using a wide spatula. Spoon onions, carrots, prunes, and some of juices on top and serve with horseradish.
*Schmaltz is available at the butcher counter of some markets, and at some butcher shops. If you don't have a pot big enough for the whole brisket, cut it in half and stack the two halves in the pot; when you add the onions, add enough additional liquid (about 2 more cups broth and the rest of the bottle of wine) so the meat is covered by three-quarters.