Rinse brisket with cold water and thoroughly pat dry.
In the bottom of a large 6-8QT slow cooker, layer the sliced onions and garlic.
Place the corned beef brisket, fat side up, over the onions. Top with pickling spice that came with brisket.
Add potatoes and carrots around the corned beef.
Pour enough liquid (1-cup) to slow cooker: should be about half way up brisket; no need to cover completely in liquid.
Cover with lid, and cook on LOW for 8 to 10 hours.
When about 2 hours of cooking time remains, remove the lid and arrange the cabbage wedges over the corned beef, potatoes and carrots.
Replace the lid and continue cooking for 2 hours, until the brisket is fork tender.
Once done, remove brisket and let cool on a cutting board 5-10 minutes (will be hot!).
Thinly slice corned beef against the grain and serve with potatoes, carrots and cabbage. Garnish with fresh parsley, if desired and serve with stone ground mustard and/or horseradish sauce.