Step 1Place the brisket in a shallow pan or container that will hold it snugly. Mix the wine, brown sugar, garlic, thyme and bay leaves and pour over the meat. Wrap with plastic wrap and refrigerate for 24 hours, turning the meat once.
Step 2Heat the oven to 325 degrees. Lift the brisket from the pan and scrape off the garlic and herbs, adding them to the marinade. Save the marinade. Pat the meat dry and season it with three-fourths-teaspoon salt and one-half-teaspoon freshly ground black pepper on each side. Warm the olive oil on the stove at medium high in a Dutch oven that fits the meat. Brown the meat evenly and carefully for 7 to 10 minutes. Add the marinade and bring to a boil. Pour in the beef broth to cover. Bring to a boil, remove from the heat and cover. Braise in the oven for 3 hours.
Step 3While the brisket is in the oven, bring a small pot of water to boil over high heat. Add the pearl onions, and blanch for about 1 minute. Remove the onions and shock in cold water. Cut off the ends of the onions, and squeeze off the outer skin. Peel, trim and quarter the turnips lengthwise.
Step 4Remove the brisket from the oven. Add the onions and turnips to the meat in the pan, spooning liquid from the pan over the brisket. Cover with foil and cook for 1 hour more, or until the turnips are fork tender.
Step 5Transfer the brisket to a cutting board, slice it against the grain in thin slices and place them on a warm platter. You will need a large spatula, as the meat may be starting to fall apart. Spoon vegetables around the meat, removing bay leaves and sprigs of thyme. Cover loosely and keep warm. Put the pan with the liquid (you will have about 6 1/2 cups) over medium to high heat. Add the cider and cider vinegar, bring to a boil, then lower the heat and reduce for about an hour until the sauce coats the back of a spoon (this makes a little more than 1 cup sauce). Taste and season the sauce as needed with salt and pepper.
Step 6Strain the sauce over the meat and vegetables and serve.