Into the lower pot of a double boiler, add water. In the upper pot, add milk. Heat through over medium heat.
Beat eggs together until light. Add sugar and mix well. Pour a small portion of hot milk into the eggs and sugar to warm and thin this portion. Pour slowly into hot milk.
Cook, stirring constantly until it will coat a spoon. Do not over cook. Add vanilla extract. Chill in refrigerator before serving.
