In a 1-2 qt. saucepan, combine apricots, water, sugar, and cinnamon stick. Bring to boil over high heat, then cover, reduce heat, gently simmer until Apricots are very tender when pierced, about 15 minutes. Discard Cinnamon. Let Apricots cool at least 1 hour. Pour into blender and add milk. Whirl until mixture is smooth. Mix in a large bowl with vanilla, milk, and nutmeg. Cover and chill at least 4 hours or until the next day. In a large bowl, beat egg whites with an electric mixer on high speed until frothy. Gradually beat in remaining sugar until whites hold stiff moist peaks. Set aside about half C. of the meringue. Gently whisk Apricot mixture into remaining meringue until smoothly blended. Stir in Rum or Brandy to taste and enough more Milk to thin to desired consistency. Pour into serving bowl and float the reserved meringue on top of the liquid. Makes 3.5 Qts. (18 servings at 6 oz. each)