Soak the tapioca in the water for about 15 minutes while you gather other ingredients.
Warm the milk, sugar, and salt in a medium saucepan over medium heat until steaming.
Stir in the soaked tapioca with its water. Simmer gently, stirring often, until the pearls start to turn translucent, 12–15 minutes.
Whisk the eggs in a bowl. Slowly ladle in a cup of the hot mixture, whisking to temper.
Pour the tempered eggs back into the saucepan. Cook, stirring constantly, until thick enough to coat a spoon, 2–3 minutes. Do not boil.
Remove from heat and stir in the vanilla. Let stand 10 minutes, then serve warm or chill until set.