In a large saucepan, combine the sugar, flour, cornstarch, mustard, salt and pepper. Gradually stir in vinegar and water. Add egg and milk. Cook and stir until mixture comes to a boil. Cook two minutes longer or until slightly thickened. Cool to room temperature, stirring several times.
In a large bowl, combine the brown sugar and cream. Stir in mayonnaise. Add cooked dressing; mix well. In several large bowls, combine the cabbage, carrots, celery and green onions. Add dressing and toss to coat. Serve immediately.