Rum-Buttered Nutmeg Logs

Wet Ingredients: In a mixing bowl, use a hand mixer or stand mixer to beat 1 cup butter (softened) and ¾ cup granulated sugar until fluffy. Beat in 1 large egg, 2 teaspoons vanilla extract and 1 teaspoon rum flavoring.
Dry Ingredients: Whisk together 3 cups all-purpose flour and 1 teaspoon ground nutmeg in a separate bowl. Add to the butter mixture, 1 cup at a time until mixed thoroughly.
Chill Dough: Remove dough from bowl and wrap in wax paper. Refrigerate for at least 1 hour.
Prep: When you are ready to make cookies, preheat oven to 350℉ and then take a small chunk of dough and warm slightly in your hands.
Cut Logs: Place some flour on a cutting board and roll out the dough until it is ½" round. Cut into 2 ½" logs.
Bake: Arrange the logs on an un-greased cookie sheet. Bake in preheated oven for 14-16 minutes. Cookies should be slightly brown on the bottom, not on the top. Remove from oven and cool on a wire rack.
Make Frosting: Beat together 3 tablespoons butter and ½ teaspoon rum flavoring (or rum). Add a ½ cup powdered sugar and beat. Add 2-3 tablespoons half and half and beat in. Gradually add 2-3 cups powdered sugar until it reaches a spreading consistency.
Frost the Logs: Spread frosting on each cookie and then run tines of a fork over the frosting to resemble bark. Sprinkle tops with nutmeg.