Tapioca Pudding

1/2 cup small pearl tapioca (it comes in a box, we use Island Tapioca brand)
3 cups whole milk (or skim milk with cream added)
1/4 teaspoon salt
2 eggs
1/2 cup of sugar
1/2 teaspoon of vanilla

Combine tapioca, milk, and salt in 1 1/2 quart pan on medium high heat. Stir until boiling. Simmer 5 minutes, uncovered at the lowest possible heat, adding sugar gradually. Beat eggs in a separate bowl. Mix in some of the hot tapioca very slowly to equalize the temperature of the two mixtures (to avoid curdling). Return eggs to pan with tapioca. Bring to a boil. Stir 3 minutes more over lowest possible heat. Stir constantly. You may cook a little longer than 3 minutes if needed to get to a nice thick pudding consistency. Cool 15 minutes. Add vanilla. Serve either warm or chilled.