1. In a medium bowl mix butter, sugar, eggs, vanilla and rum extract together. Add nutmeg and flour and mix well.
2. Cover and place in refrigerator for half an hour.
3. Roll into logs and cut into 2-inch segments. Arrange on a cookie sheet.
4. Bake at 350 degrees for 12 - 15 minutes. Cool before frosting.
Frosting
Mix first 4 ingredients together. Add milk 1 tablespoon at a time until you have the right spreading consistency. Frost the nutmeg logs.
