Combine tapioca, milk, and salt in 1 1/2 quart pan on medium-high heat.
Stir while bringing to a bare simmer. Lower the heat and cook uncovered, at the lowest possible heat, adding sugar gradually, until the tapioca pearls have plumped up and thickened. Depending on the type or brand of tapioca you are using and if you've presoaked the tapioca as some brands call for, this could take anywhere from 5 minutes to 45 minutes of cooking at a very low temperature. Stir occasionally so that the tapioca doesn't stick to the bottom of the pan.
Beat eggs in a separate bowl. Mix in some of the hot tapioca very slowly to equalize the temperature of the two mixtures (to avoid curdling).
Return eggs to pan with tapioca. Increase the heat to medium and stir for several minutes until you get a thick pudding consistency. Do not let the mixture boil or the tapioca egg custard will curdle.