In a heavy saucepan, whisk together eggs, sweetener and salt. Gradually add 2 cups of the nut milk; cook and stir often over low heat until a thermometer reads 160°-170°, about 15 minutes. Do not allow to boil. Immediately transfer to a large bowl.
Stir in vanilla, nutmeg and remaining nut milk. Place bowl in an ice-water bath, stirring until milk mixture is cool. (If mixture separates, process in a blender until smooth.) Refrigerate, covered, until cold, at least 3 hours.
To serve, beat cream until soft peaks form. Whisk gently into cooled milk mixture. If desired, sprinkle with additional nutmeg before serving. This produces a thick creamy layer that rises to the top somewhat. If you don't want that you can skip beating the cream and just add it, unbeaten, into the drink mix. This will produce a thick drink with a more storebought type consistency.