In a large mixing bowl, beat together butter and brown sugar on medium to medium-high speed until fluffy.

Add egg yolks, one at a time. Beat until well incorporated, scraping the side of the bowl as needed.

Add eggnog and rum extract.

Add flour, one cup at a time, mixing well between each addition and scraping the sides of the bowl as needed.

Cover cookie dough with plastic wrap and refrigerate for at least two hours.

Preheat oven to 325 degrees.

Form dough into 1-inch balls. Place at least two inches apart on a greased cookie sheet.

Bake for 12-16 minutes or until the bottom of the cookies are brown.

Allow cookies to cool completely on a wire rack before icing.

In a large mixing bowl, beat sugar, butter, rum extract, nutmeg, and cinnamon at low speed, increasing to medium speed once the ingredients start to come together.

Gradually add eggnog until icing reaches desired consistency.

Spread icing over the tops of the cooked cookies.

Let cookies stand until icing is set.

Store uneaten cookies in an airtight container.