Grease 9x13" baking dish with cooking spray.
Preheat oven to 350 degrees F.
In a large bowl with electric mixer, beat butter and sugar until fluffy, about 3 minutes.
Add egg and rum extract, and bet until combined.
In a separate bowl, whisk together flour, baking powder, salt, and nutmeg and whisk well to combine.
Add flour mixture to butter mixer and beat until combined.
Add eggnog and beat until combined.
Spread bar batter into prepared baking dish.
Bake for 22-25 minutes, until edges are slightly golden. The middle may not appear set, but it will continue to set as it cools! You don't want to over bake these!
Cool completely.
Make the frosting by beating butter until creamy.
Add rum extract and eggnog and beat again until well combined.
Add powdered sugar and nutmeg and beat until creamy.
Spread over cooled bars.
Cut into bars and enjoy!