Step 1Heat the oven to 350 degrees. In the bowl of a stand mixer, or in a large bowl using an electric mixer, cream together the butter and sugar. Beat in the egg, then the vanilla and rum flavoring. Beat in the nutmeg.
Step 2Slowly beat in the flour until evenly incorporated.
Step 3On a lightly floured surface, roll the dough into logs one-half-inch thick. Cut the logs into 3-inch lengths.
Step 4Bake the cookies about 1 inch apart on an ungreased baking sheet until set and faintly colored around the edges, about 12 minutes. Cool the cookies on a rack.
Step 1In a medium bowl, whisk together the butter, rum flavoring, vanilla and powdered sugar. Whisk in the milk. The frosting should have a buttercream-like consistency. Add additional milk if needed to achieve the proper consistency.
Step 2Frost the cookies with a scant half-teaspoon of frosting, marking each frosted cookie with a fork to give it "bark-like" texture.
Step 3Before the frosting sets, grate fresh nutmeg over each cookie. Store the cookies in an airtight container. The cookies can be made up to 2 months in advance (unfrozen and frosted); thaw before frosting.