Prepare the brisket: Preheat the oven to 350 degrees. Generously season the brisket with salt and pepper, then coat with the flour in a large bowl. Heat the olive oil in a large Dutch oven or ovenproof pot over medium-high heat. Brown the brisket on all sides, about 10 minutes. Transfer the meat to a plate.
Add the onions and 2 teaspoons salt to the pot and cook, stirring, until soft, about 5 minutes. Add the garlic and cook, stirring, until the onions are caramelized, about 10 more minutes. Add the tomato paste and cook about 5 more minutes. Add the wine and 1 cup water, scraping up the browned bits from the bottom of the pot. Stir in the sugar. Reduce the heat to maintain a low simmer.
Tie the celery, rosemary and bay leaves together with kitchen twine and add to the pot along with the brisket and carrots. Cut a round of parchment paper to fit inside the pot; place directly on top of the liquid, then cover with the lid. Transfer to the oven and cook 3 hours, 30 minutes.
Meanwhile, make the crust: Mince and mash the garlic with 1 teaspoon salt. Coarsely grate the horseradish. Chop the parsley with the horseradish and garlic paste until the mixture is moist.
Remove the pot from the oven, discard the parchment and transfer the meat to a rimmed baking sheet. Increase the oven temperature to 375 degrees F. Brush the top of the brisket with the mustard, then pat with the horseradish mixture. Return the meat to the pot and bake, uncovered, until the crust is golden, 30 to 35 minutes.
Transfer the brisket to a cutting board. Discard the celery-herb bundle and skim the fat from the braising liquid; thin the remaining liquid with water, if desired. Slice the meat against the grain. Serve with the carrots, onions and braising liquid.