Trim away most of the excess fat from the surface of the brisket.
In a small bowl, mix together the paprika, 1 teaspoon salt, and ½ teaspoon pepper.
Rub the spice mixture all over the meat.
Heat the olive oil in a large Dutch oven over medium-high heat.
Once hot, add the brisket, fat side down, and cook until browned on both sides, about 10 minutes, 5 minutes per side.
Remove from the Dutch oven and set aside.
Add the onions to the Dutch oven and saute over medium-high heat until the they start to brown, 6 - 8 minutes.
Stir in the garlic and saute for about 1 minute.
Pour in the wine and deglaze the pan, stirring and scraping up the browned bit on the bottom of the pan with a wooden spoon.
Stir in the stock and ketchup and bring to a boil.
Pre-heat the oven to 375°F.
Nestle the brisket, fat side up, in the Dutch oven and spoon some of the onion mixture over the meat.
Add the bay leaves and sprinkle in the thyme.
Cover and cook for 1 hour.
Meanwhile, in a large bowl, combine the apricots, carrots, orange juice, and brown sugar, tossing to coat the apricots and carrots.
Remove the Dutch oven and push the apricots and carrots into the cooking liquid around the brisket and drizzle the juice-sugar mixture over them.
Cover and cook until the brisket it tender, 2 hours longer.
Transfer the brisket to a carving board.
Cover loosely with aluminum foil to keep warm and let rest for 15 minutes.
Use a large spoon to skim as skim as much fat as possible from the surface of the cooking liquid.
Using a large, sharp knife, cut the brisket across the grain into slice, ¼-1/2-inch thick.
Arrange the slices on a platter and took with the juices and the apricots and carrots.
Serve at once and ENJOY!
Video
Notes
There a two different cuts of beef brisket, the first cut (or 'flat' cut) and the 2nd cut. The first cut is leaner and contains less fat. It slices beautifully. The 2nd cut, obviously, with more fat, will provide a flavorful sauce, as the roast slow cooks. We opt for the 1st cut, but lots of generations of home cooks have gone with the 2nd cut. Either one delivers amazing taste. As always, have your butcher trim away excess fat on the roast.