In a large saucepan combine eggnog, milk, ½ cup sugar, and cooked rice stirring constantly over med-high heat. Bring to a boil. Remove from heat.
In a small bowl stir together eggs and 2 tablespoons sugar. Temper eggs by stirring 1/8 cup of milk mixture into the eggs, add this mixture to milk mixture and return to a boil. Remove from heat. Stir in vanilla.
Serve with a sprinkling of cinnamon and/or nutmeg.