Preheat your oven to 350 then line an 8x8 inch square baking pan with parchment paper, leaving some overhang for easy removal.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy, which should take about 2-3 minutes.
½ cup butter, ¾ cup granulated sugar, ¼ cup brown sugar
Add the egg, eggnog, and vanilla extract to the butter-sugar mixture, and beat until well combined.
1 egg, ⅓ cup eggnog, 1 teaspoon vanilla extract
In a separate bowl, whisk together the flour, baking powder, nutmeg, and salt. Then add the dry ingredients to the wet ingredients and mix just until the flour mixture disappears.
2 ¼ cups all-purpose flour, ½ teaspoon baking powder, ½ teaspoon nutmeg, ½ teaspoon salt
Press the cookie dough into the prepared 8x8-inch pan, spreading it out evenly. Bake in the preheated oven for 25-27 minutes or until a toothpick inserted in the center comes out clean.