1. Soak the tapioca in water for 30 minutes, then drain.
2. In a saucepan, combine the milk, salt, and soaked tapioca. Cook over medium heat, stirring constantly until the mixture comes to a boil.
3. Reduce heat to low and simmer for 15 minutes, stirring frequently.
4. In a bowl, beat the eggs and sugar together. Slowly add a small amount of the hot tapioca mixture to the eggs to temper them, then return the egg mixture to the saucepan.
5. Cook over low heat for another 5 minutes, stirring constantly, until the pudding thickens.
6. Remove from heat and stir in the vanilla extract.
7. Let the pudding cool for 15 minutes, then transfer to serving dishes and chill in the refrigerator for at least 2 hours before serving.