In a large bowl, cream butter and brown sugar until light and fluffy. Beat in egg yolks, eggnog and extract. Gradually beat in flour. Refrigerate, covered, for at least 2 hours.
Shape into 1-in. balls; place 2 in. apart on ungreased baking sheets. Bake at 325° until bottoms are brown, 13-16 minutes. Remove to wire racks to cool completely.
In a large bowl, beat the first five frosting ingredients until blended; beat in enough eggnog to reach desired consistency. Spread over cookies; sprinkle with additional nutmeg. Let stand until set. Store in airtight containers.
This recipe was tested with commercially prepared eggnog.