In a double boiler, heat milk to room temperature (about 70 degrees F). Stir in the tapioca and salt and heat until small bubbles appear at the sides of the pan (about 170 degrees F). Cover, turn the heat to the lowest possible setting, and cook for one hour. Do not let the milk simmer or boil.
In a bowl, whisk together sugar and egg yolks. To temper the egg yolks, whisk in 2 tablespoons of the hot milk mixture, stirring constantly. Add to the milk mixture in the double boiler, increase heat to medium-low, and cook until the tapioca is thick, about 15 minutes.
Remove from heat, stir in the vanilla and let cool. Chill at least 30 minutes. The pudding will continue to thicken as it chills. Serve with whipped cream and a sprinkle of cinnamon sugar topping, if desired.
Tapioca pearls: Instant tapioca, minute tapioca, or "tapioca granules" will not work in this recipe; you want the real deal of "small pearl tapioca." Note: There isn't much standardization for white tapioca pearls, so they're available in a wide range of sizes. That's okay, because the pre-soaking step will compensate for any variations.
Cinnamon-sugar topping: Try 1 tablespoon granulated sugar + 1 teaspoon cinnamon. Mix and sprinkle over the whipped cream, and save the rest for cinnamon toast, oatmeal, or popcorn.
Yield: One recipe makes 8 servings.
Make ahead: Tapioca can be made up to 3 days before you need it; just cover and keep chilled.
Storage: Store in the refrigerator with a sheet of plastic wrap pressed right up against the surface (to prevent a skin from forming on top of the pudding).
Non-dairy: You can substitute any kind of plant-based milk: coconut milk, nut milk, almond milk, and soy milk will all work.
Brown sugar: For deeper flavor, try brown sugar in place of the granulated sugar.
Too thick: If the pudding is thicker than you prefer, add a splash of milk to the pan and stir.
DIY double boiler: To make a double boiler, you need 2 pots, one of which fits inside the other. Fill the bottom pot with one or two inches of water. Next, fit the top pot inside (make sure the water doesn't touch the upper pot) and turn on your stove to a simmer. As the water heats up and steam is released, the steam stays trapped between the two pots, which then heats the ingredients in the top pot.
Add-ins: Much like with rice pudding, you can jazz up homemade Tapioca Pudding with a variety of mix-ins and toppings. Switch up the spices (ground ginger, cardamom, nutmeg) or add fruit, nuts, or citrus zest.