Heat the oil in a large Dutch oven over medium-high heat. Add the onion, garlic, and ginger and cook, stirring occasionally, until the onion turns soft and golden, 5 to 7 minutes.
Stir in the wine, stock, gochujang, ketchup, soy sauce, brown sugar, Worcestershire sauce, and fish sauce. Add the brisket to the Dutch oven. The liquid should be somewhere between one-half to three-quarters of the way up the meat. Add more stock or water, if needed. Bring the liquid to a boil.
Cover the Dutch oven and slide it into the oven. Cook, checking every hour and spooning braising liquid over the top, until the brisket is very tender, about 3 1/2 hours. Remove the lid for the last hour of cooking.
Transfer the beef to a plate or a rimmed cutting board and tent it with foil to keep it warm.
Place the Dutch oven over medium-low heat and simmer the sauce until it is reduced to about 3 cups (it will thicken more as it cools), about 20 minutes. If you like a thicker sauce, stir in a cornstarch slurry. In a small bowl, stir together the cornstarch with 2 tablespoons (30 ml) of cold water. While the sauce is simmering, stir in half of the slurry. If the sauce still needs thickening, add the other half of the slurry.
We like to make the brisket a full day (or up to 3 days) ahead. Place the unsliced brisket back in the Dutch oven and refrigerate overnight. Once it’s cold, it’s very easy to pull the solid fat off the top of the sauce. If you like thin, neat slices of brisket, take it out of the sauce and slice it, against the grain, while it’s cold. To reheat it, place the slices back in the pot with sauce, bring it to a simmer over low and heat until it’s warmed through. You can also reheat the sliced brisket in the Dutch oven in a 275°F (135°C) oven until hot, about 15 minutes.
If you’re serving it the same day, let the brisket rest for at least 20 minutes before slicing. Make sure to use a sharp knife and cut against the grain. (If you look at the brisket, you’ll see the muscle fibers running in one direction. Cutting across these fibers shortens them, which makes for a tender piece of meat. If you slice with the grain, the brisket will be stringy and difficult to chew, no matter how you’ve cooked it.) Use a fat separator or a spoon to skim the fat off the sauce.