1) Line two baking sheets with parchment paper and set aside.
2) In the bowl of your mixer, combine all ingredients and blend on medium speed until a soft, smooth dough forms, about 2 minutes.
3) Wrap and chill the dough for 1 hour. Towards the end of the chill time, preheat the oven to 350°F.
4) Drop tablespoon-sized dough balls onto your baking sheet. A teaspoon scoop makes this job a snap. Bake the cookies for 8 to 10 minutes. The edges will be slightly browned and the cookies will be round and domed.
5) Cool the cookies completely. Prepare the icing by blending the softened butter and confectioners' sugar. Add rum one tablespoon at a time until you have a spreadable icing. Top each cookie with a dollop of icing and a dash of nutmeg. If you prefer not to use actual rum, you can use heavy cream and a few drops of rum flavoring.
Yield: Approximately 3 to 4 dozen cookies.