Heat oven to 350°. In a large bowl, beat butter, sugar, vanilla, rum flavoring and nutmeg until fluffy. Beat in egg. Beat in flour, one cup at a time until mixed well. Divide dough into 16 equal balls. Shape one ball into a 12-inch long roll. Cut into 3 inch lengths. Place 1-inch apart on an ungreased baking sheet. Repeat with remaining dough. Bake 11-13 minutes until light brown on bottom. Cool on wire racks.
For the frosting, in a small bowl, mix butter and flavorings until creamy. Add sugar and milk. Mix until smooth.
When cookies have cooled, spread a diagonal band of frosting across each cookie and sprinkle with colored sugar.
Makes 64 cookies