Cook rice according to package instructions.
In a sauce pot scald milk, then lower heat to a simmer and add cooked rice, vanilla, and sugar.
In a separate bowl, beat eggs until well mixed. Once the rice mixture begins to simmer, allow it to cool for a minute, stirring. Slowly add 2 cups of rice to bowl of eggs and mix well — repeat until all all rice has been added to eggs.
Place rice and egg mixture back into sauce pot and reduce heat to low, stirring frequently and slowly until the mixture thickens. Remember, there are eggs in this dish, be careful with letting the pot get too hot or it will curdle the eggs. Once thickened, allow it to cool in a shallow baking dish and add a pinch of salt, refrigerate and serve cold.