Rinse the tapioca pearls under cold water and drain. In a medium saucepan, soak the tapioca pearls in 1 cup of the whole milk for 30 minutes.
After soaking, add the remaining 1 cup of milk, salt, and sugar to the saucepan. Stir to combine.
Over medium heat, bring the mixture to a simmer, stirring frequently to prevent sticking. Reduce heat to low and continue to cook, stirring constantly, for 10-15 minutes or until the tapioca pearls become translucent and the mixture thickens.
Remove the saucepan from heat. In a separate bowl, gradually add a small amount of the hot tapioca mixture to the beaten eggs to temper them. Stir the egg mixture back into the saucepan with the tapioca.
Return the saucepan to medium-low heat and cook, stirring constantly, for an additional 2-3 minutes or until the pudding thickens further.
Remove from heat and stir in the vanilla extract.
Transfer the pudding to individual serving dishes or one large serving bowl. Allow the pudding to cool for a few minutes, then cover with plastic wrap and refrigerate until chilled.

Before serving, sprinkle with ground cinnamon or nutmeg if desired. Enjoy your homemade tapioca pudding!