For the cookies:

1. In a medium bowl, whisk together the flour, nutmeg and salt. Set aside.
2. In the bowl of an electric mixer, cream 2 sticks butter and granulated sugar until smooth.
3. Add egg and vanilla; beat until incorporated.
4. Add the flour mixture and beat until blended.
5. Cover and chill dough at least 1 hour and up to 24 hours.
6. When you’re ready to bake, preheat oven to 350 degrees and line two baking sheets with parchment paper.
7. Roll dough into 1 ½-inch balls (Use a #80 scoop or a tablespoon measure).
8. Arrange on prepared baking sheets spacing 2 inches apart.
9. Bake until firm to the touch and light brown on the edges, 10 minutes.
10. Transfer to a rack to cool.

For the icing:

1. Blend together powdered sugar, 2 Tbsp. butter, milk and rum and mix using a hand mixer or even a whisk.
2. Frost cooled cookies.