Place brisket in Dutch oven and cover with cold water. Cover tightly and cook 1 hour at 350°F. It's very important to simmer the meat slowly because boiling will cause meat to become tough.
Turn brisket over and continue cooking, covered, for 1 1/2 to 2 hours, or until meat is tender. Remove brisket from cooking liquid and place flat-side up, on broiler pan. Move oven rack so the 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.