Put an oven rack in the lower middle position and pre-heat the oven to 300°F.  Line a 13 x 9-inch baking dish with two 24-inch long pieces of 18-inch wide heavy duty aluminum foil, placing the sheets perpendicular to each other, fitting them into the dish, and letting the excess hang over the edges.

Pat the brisket dry with paper towels and place fat side up.  Using a dinner fork, poke holes through the fat layer about one inch apart all over the brisket.  Season both sides of the brisket with salt and pepper.

Heat about 1 teaspoon of oil in a 12-inch skillet over medium-high heat until the oil just begins to smoke.  Place the brisket, fat side up, in the skillet (the meat may come up the sides) and place a heavy pan (cast iron works well) on top of the brisket.  Cook until well-browned, about 7 minutes.  Remove the cast iron pan, turn the brisket over and cook without the weight until browned, about 5 minutes longer.  Transfer the brisket to a platter.

Pour off all but 1 Tablespoon fat from the pan (or add enough oil to make 1 Tbs.).  Stir in the onions, sugar and ¼ tsp. salt and cook over medium-high heat, stirring occasionally, until the onions are soft, 10-12 minutes.  Add the garlic and cook, stirring frequently, until fragrant, about 30 seconds, then add the tomato paste and stir to combine until paste turns darker, about 2 minutes.  Add the paprika and cayenne and cook, stirring frequently, until fragrant, about 1 minute.  Add the flour and cook, stirring constantly, until completely combined, about 2 minutes.  Add the broth, wine, bay leaves, and thyme, stirring to scrape up browned bits from pan.  Bring the mixture to a boil, reduce heat and simmer for about 5 minutes or until thickened.

Place the sauce and onions in the foil-lined dish, then place the brisket on top, fat side up.  Seal the foil and place in the oven.  Cook until a fork slips easily in and out of the meat; start checking after about 3½ hours.  Carefully open the foil (steam will escape) and let cool for 20-30 minutes.

Transfer the brisket to a large bowl, place a fine mesh strainer over the bowl and strain the sauce over the brisket. Remove the thyme sprigs and the bay leaves from the onions and put the onions in a small bowl.  Cover both bowls with plastic wrap, cut slits in the wrap and refrigerate overnight, or for up to 2 days.

About 1 hour before serving, take the brisket out of the refrigerator, place an oven rack in the lower-middle position, and preheat the oven to 350°F.  Remove the brisket from the bowl and put it on a cutting board.  Scrape off the congealed fat from the surface of the sauce, then heat the sauce in a medium saucepan over medium heat until warm.  Add the onions and the vinegar to the warmed sauce and season with salt and pepper to taste.

Slice the brisket across the grain into ¼-inch slices, place in a 13 x 9-inch baking dish, and pour the onions and sauce over the meat.  Cover the baking dish with foil, and bake until heated through, 25 to 30 minutes.