super creamy rice pudding

I'm a sucker for anything PUDDINGY - rice pudding, tapioca pudding, chocolate pudding, bread pudding mmmm mmm I LOVE PUDDING and this is great because it's quick, easy and if you get a snack attack or a sweet tooth out of nowhere you usually have all the ingredients in the house

Ingredients (doubled)

1½ cups uncooked arborio rice (apparently you can use regular white rice, I just really like arborio)
4 cups milk, divided
2/3 cup white sugar
½ teaspoon salt
2 eggs, beaten
1-2 tablespoon butter
1 teaspoon vanilla extract

Directions:

1. In a good size pot, bring 3 cups water to a boil. Add rice and stir. Reduce heat, cover and simmer for 20 minutes.
2. add 2 cups of the milk, sugar and salt. Cook over medium heat, stirring often, until thick and creamy, 15 to 20 minutes,
3. mix eggs into remaining milk and add a bit of rice mixture to milk/egg mixture to temper and stir into pot. Cook 2 minutes more, stirring constantly. Remove from heat, and stir in butter and vanilla. Serve warm.

or cold.... or hot... or room temperature hehehe