Rinse the corned beef WELL, wipe off any remaining brine with paper towels. Cut into 4 large pieces.
First, place corned beef fat side down in the bottom of the slow cooker. Add potatoes, carrots, celery, cabbage (make sure to not add too much cabbage or the lid won't close), onion slices, butter, minced garlic, pepper, and salt.
Pour the broth into the slow cooker and cover.
Cook on LOW for 8 hours or on HIGH for 4.5 hours.
Take corned beef out of the slow cooker. Remove the fat and discard. Shred corned beef and return to the slow cooker. You can cut and cube the meat instead of shredding if you want smaller pieces.