Place brisket and water in Dutch oven; cover tightly and cook 1 hour at 350 degrees (F). ( It is very important to simmer the meat slowly because boiling will cause meat to become tough.) Turn brisket over and continue cooking, covered, 1 1/2 to 2 hours, or until meat is tender. Remove brisket from cooking liquid and place, flat-side up, on rack in broiler pan so surface of meat is 3 to 4 inches from heat.
Combine honey with 1 tablespoon mustard; brush half of mixture over top of brisket and broil 3 minutes. Brush with remaining mixture and continue broiling 2 minutes, or until brisket is glazed. Meanwhile, steam cabbage 15 to 20 minutes, or until tender. Combine remaining mustard with butter and dill; spread over hot cabbage wedges. Carve brisket diagonally across the grain into thin slices and serve with cabbage.