To brine the brisket bring a large pot of water over medium heat and stir in both salts, sugar, garlic, bay leaves, cloves, mustard seeds, coriander seeds, peppercorns, and allspice, stirring until the mixture is warm and the salt and sugar is completely dissolved.
Let the brine come to room temperature then add to a container large enough to fit the brine and the brisket. Add the brisket and weight the meat down with something heavy like a plate. Cover and refrigerate for 5 days, turning once a day.
When ready to cook the brisket, or if using a store bought packaged corned beef brisket, remove it from the brine and rinse it completely.
Heat oven to 300ºF. Place the brisket in a Dutch oven or baking dish large enough to hold the brisket.
Pour the beer over the top. Add just enough water until the brisket is covered. Tightly cover with aluminum foil and transfer to the oven. Let cook for 2½ hours.
Add the potatoes and carrots into the liquid around the beef then add the cabbage over the top. Cover and cook until the brisket is tender enough that a fork can easily be inserted into the meat, about an additional hour.
Let cool then remove to a cutting board and thinly slice the meat against the grain into ½” slices and serve with the potatoes, carrots and cabbage.
Keep the meat in the cooking liquid until ready to use, for up to 3 days.