Place the water and tapioca pearls in a 1 1/2 quart pot. Let stand for 30 minutes until the pearls are plump and have absorbed the water.

Turn the heat to medium-high and add the milk and salt. Stir continuously while bringing the mixture to a bare simmer.

Reduce the heat to low, add the sugar, and cook uncovered. Stir frequently to prevent the tapioca from sticking to the bottom of the pan. Continue cooking until the tapioca pearls are plump and the mixture has thickened, about 5 minutes.

In a separate bowl, beat the eggs. Gradually whisk in about 1/2 cup of the hot tapioca mixture to temper the eggs and prevent curdling.

Pour the tempered egg mixture back into the pot with the remaining tapioca. Increase the heat to medium and stir constantly for several minutes until the mixture thickens and coats the back of a wooden spoon. Be sure not to let it boil.

Remove from heat and let the pudding cool for 15 minutes.

Stir in the vanilla extract.

Serve the tapioca pudding warm or cold. Enjoy!