Preheat the oven to 350℉. Line baking sheets with parchment paper.

In a large bowl, cream together the softened butter, sugar, and brown sugar for 1 minute using an electric handheld mixer or a stand mixer fitted with the paddle attachment on high speed.

Add the egg, vanilla, and rum extract and continue creaming until fluffy. Add the flour and nutmeg and mix at low speed just until fully incorporated.

Scoop the cookie dough into 1 tablespoon-sized portions and roll well to form smooth, uniform balls. Place on the prepared baking sheet, leaving 2 inches between each cookie for spreading room.

Bake in the preheated oven for 12-15 minutes or until slightly golden on the bottoms. Let cool fully before topping with the icing.

In a bowl, whisk together the powdered sugar, nutmeg, and rum extract. Add whipping cream gradually, starting with 2 tablespoons and then adding 1-2 more tablespoons or until a smooth, no-too-runny glaze/icing consistency is reached. Spoon on top of the cooled cookies and spread around slightly with the back of a spoon. Enjoy!