In a very large pot, combine the water, kosher salt, brown sugar, pink curing salt, garlic, ginger, cinnamon stick, bay leaves, mustard seeds, peppercorns, allspice berries, juniper berries, and cloves. Stir and bring to a boil over high heat.
Once the brine is boiling, remove from the heat and add the ice to bring the temperature below 45˚F (7˚C).
Place the brisket in a large plastic storage container with a lid. Pour the cooled brine over the meat. Cover and brine the beef in the refrigerator for 5–7 days, flipping once a day.
Once the brisket is brined, remove the beef from the liquid and transfer to a pot large enough for it to sit flat on the bottom. Add the onion, celery, carrot, ginger beer, and beer. Bring to a boil over high heat, then reduce the heat to low, cover, and gently simmer for 2½–3 hours, or until the meat is fork-tender. Remove the meat from the pot and let cool. If making corned beef and cabbage, reserve the cooking liquid. Otherwise, discard.
Thinly slice the brisket against the grain for sandwiches or corned beef and cabbage, or dice for corned beef hash.
Return the corned beef cooking liquid to a boil over medium-high heat. (If starting with new cooking liquid, combine the chicken broth, water, chopped carrots, celery, and onion in a large pot and bring to a boil.)
Once the cooking liquid is boiling, add the potatoes and cook for 10 minutes, until half-cooked. Add the halved carrots and cabbage, cover, and cook for 10–15 minutes more, until the vegetables are tender.
Transfer the vegetables to a serving platter with the sliced brisket and ladle the cooking liquid over.