Preheat oven to 375 degrees. Line baking sheet with parchment paper or silicone mats.
Cut cold butter into tablespoon chunks, add to electric mixer. Beat on low until butter is somewhat softened.
Add sugars and cream on low until well combined.
Add egg, eggnog, vanilla extract, and rum extract. Mixed until well combined, scraping the sides and bottom of the bowl.
Sift together dry ingredients. Add to wet ingredients, turn mixer on low and mix until well combined.