Place corned Beef in a large stockpot; add water, onion, celery, pickling spice and garlic cloves. Bring to a boil. Cover, reduce heat, and simmer 3 hours. Remove brisket from pot. Set aside.
Strain cooking liquid into 2 large bowls; discard solids. Return liquid to the pot.
Add caraway seeds and cabbage; bring to a boil. Reduce heat; simmer 20 minutes. Drain.
While cabbage is cooking, place potatoes and carrots in a large Dutch oven. Cover with water. Bring to a boil; cook 20 minutes or until tender. Drain. Return potatoes and carrots to pan. Stir in parsley, butter, lemon rind, lemon juice and pepper; toss to coat.
Optional: Preheat broiler. Place corned beef on the rack of a broiler pan or roasting pan coated with cooking spray; place rack in pan. Combine breadcrumbs and horseradish. Spread mustard over one side of corned beef. Press breadcrumb mixture onto the mustard. Broil 3 minutes or until lightly browned.
Serve corned beef with cabbage, potatoes and carrots.