Gradually add sugar and beat until light and fluffy.
Then add the egg, vanilla, and rum.
Fold in flour, nutmeg, and salt.
Spread some sugar out on a surface or cutting board to make a sugar board. Roll dough on sugar board to about 5/8 inch roll and then cut in 2” pieces. The end result will look like a log.
Bake at 350 degrees in a preheated oven for 10 to 12 minutes. Let the cookies cool before frosting.
Frosting
Beat together all ingredients until smooth.
For thinner or thicker frosting add more or less rum. The strong rum taste will go away after the frosting dries.