Using a mixer, blend together the butter and sugar until creamy
Add in vanilla and rum extracts and egg and combine
In a separate bowl, combine flour, corn starch and baking soda
Slowly add in the dry ingredients into the mixer, alternating between adding flour mixture and eggnog
Batter will become very thick
Once batter is well combined, refrigerate for an hour or longer
Preheat oven to 350 F
Remove batter from refrigerator and grease a cookie sheet
In a small bowl. combine extra sugar and nutmeg and set aside
Roll dough into 1- 1 1/2 inch balls using your hands and gently flatten a little with your palms Roll each ball around in the sugar mixture to coat
Place the dough evenly spaced apart from each other on the cookie sheet and bake for 10-12 minutes
Remove cookies from oven and allow to finish cooling on a wire rack
While cookies are cooling, wisk together powdered sugar, eggnog, vanilla and nutmeg for glaze and drizzle on top of each *completely cooled* cookie
Enjoy!