Layer the aromatics: Place the onion and garlic in the bottom of the slow cooker to create a flavor base and keep the meat elevated slightly.
Add the brisket: Rinse the corned beef under cold water to remove excess brine, then pat dry. Place it fat-side up on top of the onions. Sprinkle the contents of the spice packet over the meat.
Add liquid and seasoning: Pour in the beef broth until it reaches about 1 inch up the sides.
Add the brown sugar, vinegar, bay leaf, and a few grinds of black pepper.
Start the cook: Cover and cook on Low for 8 to 10 hours, or on High for 4 to 5 hours. Low is best for tenderness.
Add root vegetables: About 3 hours before the end (on Low) or 1.5 hours before the end (on High), tuck the potatoes and carrots around the meat. Spoon some liquid over the top.
Add cabbage: About 1 to 1.5 hours before serving (on Low) or 45 minutes before (on High), add the cabbage wedges on top.
Re-cover and continue cooking until tender.
Rest and slice: Transfer the brisket to a cutting board and let it rest for 10 minutes. Slice against the grain for maximum tenderness.
Serve: Arrange slices of corned beef with the potatoes, carrots, and cabbage. Ladle some cooking liquid over everything.
Garnish with parsley and serve with mustard or horseradish.