Combine eggs, sugar, and salt in a medium mixing bowl; beat with a wire whisk until well combined. Add milk and vanilla, beating until well blended.
Pour custard evenly into six 6- ounce custard cups. Sprinkle top of each custard with ground nutmeg. Place custard cups in a 13- x 9- x 2 - inch baking pan. Add warm water to pan to a depth of 1 inch.
Bake at 325° for 1 hour or until a knife inserted between center and edge of custard comes out clean. Remove cups from water; serve hot or chilled.