Melt the butter in a 12-inch cast iron skillet set over medium heat. Add the bell pepper and cook until it begins to brown slightly, approximately 5 to 6 minutes. Add the garlic, corned beef and cabbage, thyme, oregano and black pepper to the skillet and stir to combine. Once combined, spread the hash evenly over the pan and firmly press down with a spatula. Place a heavy lid, heatproof plate or second pan directly atop the hash and allow to cook until browned, approximately 10 minutes. After 10 minutes stir mixture, press down again, top with the lid and allow to cook another 5 to 6 minutes, or until browned. Serve immediately.
*Cook's note: Brisket should be prepared through the brining stage, but not cooked.
Place the corned beef, pepper, allspice, bay leaves and salt into a large 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 for an additional 15 to 20 minutes until the potatoes and cabbage are tender. Remove the bay leaves and serve immediately.
Place the water into a large 6 to 8 quart stockpot along with salt, sugar, saltpeter, 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 45 degrees F. 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 from the brine and rinse well under cool water. Place the brisket into a pot just large enough to hold the meat, add the onion, carrot and celery and cover with water by 1-inch. Set over high heat and bring to a boil. Reduce the heat to low, cover and gently simmer for 2 1/2 to 3 hours or until the meat is fork tender. Remove from the pot and thinly slice across the grain.