-
Preheat the oven to 350 degrees F (180 degrees C). Line an 8x8-inch square pan with enough parchment paper to have overhang on all sides.
-
For blondies, whisk melted butter, white sugar, brown sugar, salt, nutmeg, and ground cinnamon together in a large bowl until combined. Add egg, vanilla, and rum extract and whisk until smooth. Add eggnog and whisk until thoroughly incorporated. Whisk in flour and baking soda just until combined. Pour batter into the prepared pan and spread into an even layer.
-
Bake in the preheated oven until blondies are golden brown and begin to pull away from the sides of the pan, 30 to 35 minutes. Cool blondies in the pan for 15 minutes, then remove to a wire rack to cool completely, about 30 minutes. Optional: use a spatula to press down the puffed-up sides of the blondies while they are still warm to make a flatter, more even surface to frost.
-
For frosting, beat butter and cream cheese together in a bowl with an electric mixer until completely smooth. Add 1 cup confectioner's sugar, vanilla, nutmeg, and salt and beat until completely smooth. Add eggnog; beat until combined. Beat in remaining confectioner's sugar; turn mixer speed up to medium-high and beat frosting until light and fluffy, 2 to 3 minutes.
-
Pour frosting over cooled blondies and spread into an even layer. Sprinkle with nutmeg. Cut into 16 bars.