Preheat oven to 350°. Sprinkle all sides of brisket pieces with salt and pepper. Cook brisket, in batches, in hot oil in an ovenproof Dutch oven over medium-high heat until browned on all sides (about 15 minutes). Transfer to a plate, reserving drippings in Dutch oven.
Add white onions and shallots to hot drippings in Dutch oven, and sprinkle with sugar. Cook over medium heat, stirring often, 25 minutes or until onions are soft and caramelized. Stir in wine, 1 tsp. rosemary, and brisket. Top with cipollini onions; cover.
Bake at 350° for 4 hours or until brisket is tender. Remove from oven, and let stand, covered, 30 minutes. Transfer brisket to a cutting board and onions to a large bowl, reserving liquid in Dutch oven. Cover brisket and onions loosely with aluminum foil.
Bring reserved liquid to a boil over high heat, stirring often; boil, stirring often, 10 minutes or until liquid is reduced by half. Stir in cooked onions and remaining 1/2 tsp. rosemary.
Cut brisket across the grain into thick slices. Serve with onion mixture.