Shred the cabbage.
Beat the egg in a bowl. Mix in the flour, salt, mustard, sugar and pepper until smooth.
Melt the butter in the top of a double boiler over boiling water and stir in egg mixture and milk. Slowly add the vinegar, beating constantly, and cook 5 minutes, or until sauce is thick.
Cook cabbage in salted water to cover for 6 minutes. Do not overcook. Cabbage should be crisp. Drain well.
Mix cabbage and sauce and serve hot.