Make the corned beef: Place the water into a large (6- to 8-quart) stockpot along with both salts, sugar, cinnamon stick, mustard seeds, peppercorns, cloves, allspice, juniper berries, bay leaves and ginger. Cook over high heat until the salt and sugar have dissolved. Remove from the heat and add the ice. Stir until the ice has melted. If necessary, place the brine into the refrigerator until it reaches a temperature of 45ºF.
Once it has cooled, place the brisket in a 2-gallon zip top bag and add the brine. Seal and lay flat inside a container, cover, and place in the refrigerator for 10 days. Check daily to make sure the beef is completely submerged and stir the brine. After 10 days, remove the beef from the brine and rinse well under cool water.
Make the corned beef and cabbage: Combine the corned beef, pepper, allspice, bay leaves, and salt in an 8-quart pot along with 3 quarts of water. Cover and set over high heat. Bring to a boil, decrease the heat to low and cook at a low simmer for 2 1/2 hours.
After 2 1/2 hours, add the carrots, onions, potatoes, and celery. Return to a simmer and cook uncovered for 15 minutes. After 15 minutes, add the cabbage and cook until the potatoes and cabbage are tender, an additional 15 to 20 minutes. Remove the bay leaves and serve immediately.