Preheat oven to 350 F. Line two large baking sheets with parchment paper or silicone mat. Set aside.

In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg and salt. Set aside.

Cream butter and sugars together for about 3 minutes, until light and fluffy. Beat in egg yolk, vanilla, rum extract and eggnog, until combined.

Turn mixer to low and slowly add the dry ingredients, until just combined.

Scoop about 1 1/2 tablespoonful and drop onto prepared baking sheets 2-inches apart. Place one baking sheet in the fridge to chill while you bake the other.

Bake one sheet at a time in preheated oven for 10 - 12 minutes. Remove baking sheet from oven and allow cookies to cool on baking sheet for 5 minutes then transfer to a wire rack to cool completely.

Cream butter for about 3 minutes, until light and fluffy. Slowly add powdered sugar and beat until combined. Add rum extract, cinnamon, nutmeg and rum extract.

Add eggnog, one tablespoon at a time, until desired consistency or flavor is reached.

Beat for an addition two minutes smooth. Frost cooled cookies and add sprinkles if desired.