Start by rinsing the tapioca pearls under cold water and draining them. Soak these pearls in a medium saucepan with 1 cup of milk for about 30 minutes.
Introduce the remaining milk, salt, and sugar to the saucepan, mixing well.
Gradually heat the mixture to a gentle simmer over medium heat, ensuring frequent stirring to avoid sticking. Once simmering, dial down the heat and continue stirring for another 10-15 minutes. The mixture should thicken and the tapioca pearls become translucent.
Off the heat, carefully blend a portion of the tapioca mix into the beaten eggs to temper them. Reintroduce this tempered egg mix back into the main saucepan.
Over medium-low heat, stir the combined mixture for another 2-3 minutes, allowing it to thicken. Finish by blending in the vanilla extract.
Distribute the pudding either into individual dishes or a single large bowl. Let it sit briefly, then seal with plastic wrap and refrigerate till it’s cool and set.