In a 2- to 3-quart saucepan, soak tapioca in water for 30 minutes.
Add milk, salt, egg yolks and granulated and brown sugar to the tapioca and stir over medium heat until it boils.
Reduce heat to a low simmer and cook, uncovered, 5 to 10 minutes or until very thick.
Stir in vanilla and nutmeg.
Transfer pudding to heat-proof bowl (tapioca will thicken as it cools).
Cover tightly and refrigerate until set, at least 1 hour.