In a medium bowl, combine 2 cups of all-purpose flour and 1 teaspoon of freshly grated nutmeg.

In a separate bowl, cream together 1 cup of softened unsalted butter, 1 cup of granulated sugar, 1 teaspoon of vanilla extract, and 1 teaspoon of rum extract until fluffy.

Add in one room temperature egg and blend smoothly, then gradually add in the dry ingredients until a soft dough forms, approximately 2-3 minutes.

Cover the dough with plastic wrap and refrigerate for about 30 minutes.

Preheat your oven to 350°F (175°C).

Scoop portions of dough and roll them into logs about 1/2 inch in diameter. Cut into 2-inch sections and place on an ungreased baking sheet.

Bake in the preheated oven for 12-15 minutes until golden around the edges but soft in the center.

Let cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

Whisk together 1 cup of powdered sugar, 2 tablespoons of milk, 1 teaspoon of vanilla extract, and 1/2 teaspoon of rum extract for the icing.

Adjust the icing consistency before generously frosting each cookie once cooled.

Sprinkle a pinch of freshly grated nutmeg on top before serving.

Allow the icing to set for about 15 minutes before serving or storing the cookies.