In a mixer fitted with a paddle attachment beat the butter and sugar until light and fluffy. Add the egg and beat well. Then add the eggnog and mix again.

Sift together the flour, baking soda, baking powder, salt, cinnamon and nutmeg. Then turn the mixer on low and slowly add the flour mixture to the wet ingredients until everything is just combined. Cover dough with plastic wrap and chill it for at least two hours.

Preheat the oven to 350ºF. Drop dough by the round teaspoonful onto lined cookie sheets. Bake one sheet at a time for 10 to 12 minutes, or until the tops are lightly golden. Cool cookies on a wire rack.

To make the icing stir together the confectioners’ sugar, eggnog, rum and nutmeg. Icing the cookies when cooled. Sprinkle cookies lightly with nutmeg before the icing dries.