Heat oven to 350. Place parchment paper on cookie sheets. In bowl, combine flour, baking powder, cinnamon and salt.
In lg bowl, beat 1 and 1/2 sticks butter, sugar and brown sugar until creamy. Beat in egg yolks, 1/2 cup eggnog, 1 tsp rum extract and vanilla. Slowly beat in flour mix until combined. Place heaping tsp of dough onto baking sheets. Bake 11-13 mins, or until light golden on bottom. Let cool on racks.
In another lg bowl, Beat 1 stick butter, 4 tbsp eggnog and remaining rum extract until creamy. Slowly beat in powdered sugar until smooth. Frost cookies and sprinkle each cookie w/ a small pinch of nutmeg.