In a medium saucepan, soak the tapioca in 3/4 cup of milk for 1 hour.

After soaking, whisk in the egg yolks, salt, sugar, and the remaining 1 3/4 cups of milk into the saucepan with the tapioca mixture.

Place the saucepan over medium heat and slowly bring the mixture to a simmer, stirring constantly to prevent sticking. This should take approximately 15 minutes.

Once simmering, reduce the heat to low and continue to cook, stirring frequently, until the tapioca pearls are translucent and the mixture has thickened, about 20 minutes.

Remove from heat and stir in the vanilla extract.

Serve the pudding warm, or let it cool and then refrigerate to serve chilled.