Rebecca Gottfred, 1994 first-place winner, made these cookies with her sister in their annual pre-Christmas baking session. Both of their families declared them a yearly must. The recipe doubles and triples easily, and the baked cookies freeze well. Reprinted with permission from Holiday Cookies by the Chicago Tribune staff, Agate Surrey, November 2014.
Beat butter in large bowl of electric mixer until light; beat in sugar until fluffy. Beat in egg, vanilla and salt; beat well. Stir in flour and nutmeg until well mixed. Refrigerate dough, covered, 1 hour.
Preheat the oven to 350 degrees F. Have two ungreased baking sheets ready.
Shape the dough into 1-inch diameter balls. Place 2 inches apart on baking sheets. Press down centers with thumb. Bake until barely golden, about 12 minutes. Cool on wire racks.
Beat the butter until light. Beat in the confectioners sugar until fluffy. Add the rum extract to taste. Beat well. Fill a pastry bag fitted with a medium star tip with the filling. Pipe a star into the center of each cookie. Sprinkle with nutmeg. Chill until filling firms, 15 minutes.