1. Preheat the oven to 350F and set an oven rack in the middle position.
2. Season the brisket on both sides with the salt and pepper. Lightly dust with the flour, turning to coat both sides evenly.
3. In a heavy flameproof roasting pan or ovenproof enameled cast-iron pot just large enough to hold the brisket, carrots, and dried fruits snugly, heat the oil over medium-high heat. Add the brisket to the pan, fatty-side down, and sear until browned, 5 to 7 minutes. Using a pair of tongs and a large fork, flip the brisket over and sear the other side in the same manner.
4. Transfer the brisket to a platter, and then add the onions to the pan. (If the pan seems dry, add a few tablespoons of water.) Cook, stirring occasionally with a wooden spoon and scraping up any browned bits stuck to the bottom of the pan, until the onions are softened and golden brown, 10 to 15 minutes.
5. Add the brown sugar, paprika, cumin, ginger, coriander, cinnamon, and cayenne to the onions and cook, stirring constantly, for 1 minute more. Add 1 cup water and scrape up any browned bits from the bottom of the pan.
6. Remove from the heat and place the brisket, fatty-side up, and any accumulated juices from the platter on top of the onions. Spread the tomato paste evenly over the brisket, and then scatter the garlic around it. Cover the pan very tightly with heavy-duty aluminum foil or a lid, transfer to the oven, and cook for 1 ½ hours.
7. Carefully transfer the brisket to a cutting board (leave the oven on). Using an electric or very sharp knife, cut the meat across the grain on a diagonal into thin slices (aim for ⅛ to ¼ in thick). Return the slices to the pot, overlapping them at an angle so that you can see a bit of the top edge of each slice. The end result should resemble the original unsliced brisket leaning slightly backward. Scatter the carrots, apricots, prunes, and capers around the edges of the pot and baste with the sauce; cover tightly with the foil or lid and return to the oven.
8. Lower the heat to 325F and cook the brisket until it is fork-tender, 1 ¾ to 2 ½ hours. Transfer the brisket to a serving platter, and then sprinkle with parsley. If you’re not planning to serve the brisket right away, let it cool to room temperature and then cover and refrigerate until ready to serve.