Place 1 cup of water and 1/2 cup small 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 on the heat to medium-high. Pour in 2 & 1/2 cups whole milk and 1/4 teaspoon coarse salt; stir while bringing to a bare simmer.
Reduce the heat to low, add in 1/2 cup sugar and cook, uncovered, stirring frequently (so the tapioca doesn’t stick to the bottom of the pan), until the tapioca pearls have plumped and thickened, about 5 minutes.
In a separate bowl or measuring cup, beat 2 large eggs. Slowly whisk in about 1/2 cup of the hot tapioca (this equalizes the temperature between the two mixtures to avoid curdling.)
Pour the egg mixture into the pot with the rest of the tapioca; increase heat to medium and stir for several minutes until you get a thick pudding consistency that coats the back of a wooden spoon. (Do not let mixture boil.)
Take off the heat and cool for 15 minutes.
Stir in 1 teaspoon vanilla.
Serve either warm or cold and enjoy!
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Notes
Not all brands of tapioca pearls are the same. Different brands of tapioca call for different instructions, so pay attention to the packaging - some small tapioca requires the pearls to soak overnight. If you don't need to soak them overnight and also want to skip step 1, you'll need to increase the amount of milk in this recipe to 3 cups. You will also likely need to cook the tapioca for a lot longer than 5 minutes (up to 45 minutes over very low heat.)Optional mix-ins. Feel free to add in a bit of unsweetened cocoa powder if you enjoy a chocolate taste. Raisins and cinnamon are also wonderful additions.Make it fluffier. For a lighter, fluffier tapioca pudding, you can separate the eggs; use the egg yolks to stir in with the hot tapioca. Once it becomes thick, beat the egg whites in a separate bowl until soft peaks form. Remove the pudding from the stove and fold in the whipped egg whites.Non dairy version. I personally have not tried replacing the whole milk with something non-dairy, but some comments say they have had success using almond milk or coconut milk instead.