Preheat oven to 350 degrees F. Line two baking sheets with parchment paper and set aside.
In the bowl of a stand mixer, cream together butter and both sugars. Mix on medium speed until light in color and fluffy.
Add in egg yolks, vanilla, rum extract, and eggnog. Mix well.
With the mixer turned off, add flour, baking powder, salt, nutmeg, and cinnamon. Slowly mix on low and then medium until a soft dough forms and mixed well.
Use a cookie scoop to scoop out cookies and place directly on prepared baking sheets. You do not need to roll these in a ball.
Bake 12 cookies per sheet for 10-11 minutes, just until set and only the bottoms lightly browned.
Let cookies cool completely on a cooling rack before frosting.
To make the frosting, cream together butter, eggnog and rum extract until fluffy. Slowly add in powdered sugar while mixing on low. Turn speed to medium and beat until smooth and creamy.
Frost cooled cookies. Sprinkle lightly with cinnamon. Enjoy!