Put oven rack in middle position and preheat oven to 350°F.
Slice onions across in thin slices (no need to chop), add the oil to your large roasting pan, straddled across two burners and heat to medium heat. Add onions and brown, moving them around to get a little color all over.
While onions are getting some color (about 3 - 5 minutes), rub brisket all over with 1 teaspoon salt and ½ teaspoon pepper. Push the onions to the edges of your pan, turn heat up to medium to medium high and place the brisket fat side down into the pan. Brown on both sides, about 5 minutes per side.
While the brisket is browning, combine the wine, stock and vinegar to become the braising liquid.
Remove the pan from heat, pour the braising liquid over the brisket and onions. Cover pan tightly with heavy-duty foil and braise brisket in oven 2 hours.
After 2 hours, remove the pan from the oven carefully and place on a protected counter. At this point, remove the meat to a cutting board and slice it across the grain. Add the sliced meat back into the pan along with the dried fruit, carrots and potatoes. Sprinkle the rest of the salt and pepper over the meat and vegetables. Cook for about one more hour, covered. Check and if meat and vegetables feel fork tender, it's done. If not, cook in half hour increments until it is.
If not eating immediately, refrigerate covered for up to two days or freeze.
To reheat, put oven rack in middle position and preheat oven to 350°F. Discard as much fat as possible from surface of vegetables and sauce, then cover with foil, place in oven until heated through, about 40 minutes. Check the sauce for seasoning and add any salt and pepper as needed once it is warm.
If the oven is not available and your meat is in a pan that is stove-top safe, you can reheat on medium low on the stove-top.