Combine all ingredients except for beef brisket in a pot over medium-high heat. Cook until salt & sugar has dissolved. Remove from heat & let cool to room temperature. Once the mixture has cooled place in refrigerator to chill.
Place the brisket in a resealable plastic bag and add the brine. Place the bag in a container and store in the refrigerator for 6-7 days.
Preheat oven to 300° F. Remove the brisket from the brine and rinse with cold water. Place the brisket, onion, garlic, bay leaves & spices in a large pot and cover with water. Bring to a boil and then reduce to a simmer. Cover with a lid and place in oven. Cook at 300 degrees for 3-4 hours.
Remove the meat and cover it with foil to keep warm. Add the cabbage, carrots & potatoes to the pot; place over medium-high heat and bring to a boil. Reduce to a simmer and cook until vegetables are tender, about 20 minutes.
Slice the corned beef against the grain. Serve with vegetables & broth.