Add the butter and white sugar to the large bowl of a stand mixer fitted with the paddle attachment, and cream them together.
Add the nutmeg, egg, vanilla, and rum extract, and mix thoroughly.
Add in the flour and combine, scraping down the sides of the bowl.
Use a tablespoon or cookie scoop to make the cookies and roll the cookie dough into balls, and press to flatten on a cookie sheet. Bake at 350 degrees for about 10 min. until golden brown around the edges. Cool completely on a wire rack.
To make the icing, cream the butter until light and fluffy.
Add in 2 cups of the powdered sugar, and extracts, and mix well.
Add in cream and last cup of icing sugar and combine well.
Frost the tops of the cookies, and sprinkle with a tiny bit of fresh grated nutmeg.