Rinse the corned beef brisket thoroughly under cold water to remove excess salt brine. Pat dry and cut into 1-inch bite-sized cubes.
Place the cubed beef, potatoes, carrots, celery, onion, and garlic into a 6-quart slow cooker.
Pour in the beef broth. Add the pickling spice and bay leaves. Stir gently to combine.
Cover and cook on LOW for 7 to 8 hours, or until the beef and vegetables are tender.
About 45 minutes to 1 hour before serving, stir in the chopped cabbage. Cover and continue cooking until the cabbage is wilted and tender but not mushy.
Remove the bay leaves. Taste the broth and season with black pepper if needed (additional salt is rarely necessary).
Ladle into bowls and garnish with fresh chopped parsley.