Rum and Nutmeg Logs

I received this recipe from a coworker.  I had never actually had any that were baked by the originator of this recipe, but I have heard raves about them for years, so I had to give them a go.  They are fantastic.  Please note - the alcohol does not bake off in the frosting, so 2 tsp of rum flavoring can be used.

  1 Cup Butter, Softened                                                            ___Frosting___

  3/4 Cup White Sugar                                                                3 Tbl Butter

  2 Tsp Vanilla                                                                           2 1/2 Cups Confectioners Sugar

  1 Large Egg                                                                              1/2 Tsp Vanilla

  2 Tsp Rum                                                                               2 Tbl Milk

  3 Cups All Purpose Flour                                                         1/4 Cup Rum

  1 Tsp Nutmeg, Ground                                                           

Preheat oven to 350 degrees.

Cream together butter and sugar.  Stir in vanilla, egg, rum and nutmeg.  Mix well and add flour.

Roll into 1/2 inch logs and cut into three inch pieces.  Place on a silicone baking mat or non stick foil and bake 12 to 15 minutes.  Let cool completely.

Frosting:  Cream together Butter, Sugar, Vanilla, Milk and 2 Tbl Rum.  Continue adding rum until desired consistency is reached - I used 4 Tbl total.  Spread over cooled cookies.