In a medium saucepan, combine the whole milk, quick-cooking tapioca, granulated sugar, and salt.

Place the saucepan over medium heat and bring the mixture to a gentle boil, stirring constantly to prevent scorching.

Once the mixture begins to boil, reduce the heat to low and continue cooking for about 5 minutes, stirring frequently, until the tapioca begins to soften and the mixture thickens slightly.

Place the beaten eggs in a medium bowl. Slowly whisk about 1 cup of the hot milk mixture into the eggs, adding only a small amount at a time to temper them.

Gradually pour the warmed egg mixture back into the saucepan while stirring constantly.

Increase the heat slightly to medium-low and bring the pudding to a gentle simmer. Cook for about 2 minutes, stirring continuously, until the mixture is thick enough to coat the back of a spoon.

Remove the saucepan from the heat and stir in the vanilla extract.

Serve the pudding warm, or transfer it to individual bowls or one large serving dish and refrigerate for 2–3 hours until chilled.