In a glass bowl, microwave the white chocolate, butter, and eggnog about 90 seconds, stirring every 30 seconds until melted and smooth.
Mix in the sugar, eggs, salt, and rum extract.
Stir in the flour just until incorporated - you don't want to mix too much air into the batter.
Spread evenly into a 9x13" greased pan. Bake for 18-20 minutes or until toothpick inserted into the center comes out clean or with fudgy crumbs. Be careful not to over bake or the brownies will not be fudgy. Let cool completely.
Glaze
In a medium bowl, whisk together the powdered sugar and eggnog until smooth. You want a thick, glue like consistency. Add more eggnog if too thick. Spread over cooled brownies, and sprinkle a bit of nutmeg on top, if desired. Store in the refrigerator.