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, remove it from heat to allow it to cool for a minute, stirring occasionally. Slowly add 2 cups of rice to bowl of eggs and mix well — repeat until all rice has been added to the 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, remove from heat and allow it to cool. Pour into a shallow baking dish, add a pinch of salt, refrigerate. Serve cold.