Fill the lower pan of a double boiler 1/3 full of water, and bring to a low boil. Pour milk into upper pot, and place over boiling water. Heat until small bubbles form around the edges of the milk. Stir in sugar, and continue stirring until it dissolves.
In a small bowl, beat the eggs until light yellow. Remove about 1/2 cup hot milk, and gradually stir it into the eggs. Slowly mix the egg mixture into the milk in the pan.
Mix together cornstarch and water; slowly stir into custard. Bring custard to a boil, and remove from heat. Stir in vanilla. Serve warm or chilled.