Rinse off the brine. Preheat an oven to 325°F (160°C). Thoroughly rinse the brisket to remove the brining liquid, then transfer to a large pot and cover with cold water. Allow the brisket to soak for 10-15 minutes before proceeding.
Meanwhile, make the spice rub. Place the spices in a mortar: 2 Tbsp whole peppercorns, 2 Tbsp coriander seeds, 1 Tbsp dill seeds, 1 Tbsp allspice seeds, and 1 tsp crushed red pepper flakes. Use a pestle to grind coarsely, then set aside.
Dry the brisket. Remove the brisket from the pot, then dry on all sides with paper towels. Drain and dry the Dutch oven. Return the brisket to the Dutch oven, fat side up. If the brisket is large, you can cook it in a roasting pan or simply cut it in half to help it fit.
Add mustard and spices. Brush all except for 2 Tbsp of the mustard on top of and on the sides of the brisket. Sprinkle the spice blend evenly over the top. Follow this by sprinkling 1 cup of brown sugar (reserve the remaining ¼ cup for later) on top of the beef.
Add onions. Place the onion wedges around the beef, then scatter the smashed garlic cloves on the side. Add 2 bay leaves.
Add liquid. Pour 1 (12oz) can of beer around the seasoned corned beef, then add enough beef broth (or water) to come up ⅔ of the way. Cover with a tight fitting lid.
Cook the corned beef. Transfer to an oven and cook for 2½ hours. Carefully remove from the oven, then scatter the potatoes, carrots, and cabbage wedges around the meat. Submerge them as best you can in the liquid. Cover tightly, then return to the oven for an additional 1½ - 2 hours or until the brisket reaches an internal temperature of 185°F (85°C) and is very tender. A good rule of thumb is to allow 1 hour per pound of meat, but to begin checking a little earlier. The cook time will vary based on the thickness of the brisket. Remove from the oven.
Preheat the broiler. Place an oven rack about 4 inches below the heating unit, then set the broiler to high.
Broil the corned beef. Using two metal spatulas, carefully transfer the corned beef to a foil-lined baking sheet. Place the remaining 2 Tbsp mustard and 3 Tbsp brown sugar in a mixing bowl with ¼ cup of the cooking liquid. Stir well, then pour (or brush) all over the top of the corned beef. Cook under the broiler for about 5-7 minutes, rotating the pan once halfway through, until the top is caramelized all over. Keep a close eye on it, some broilers are very strong!
Let the meat rest. Before slicing, allow the corned beef to rest for at least 20 minutes. Use a sharp knife to cut into thick slices against the grain. Serve with the vegetables and a bit of the braising liquid spooned on top. Enjoy!