Eggnog Cookies with Rum Glaze

Description
These soft, thin cookies are ideal for the holidays because they can be made in advance and frozen. Plus, because the recipe makes 10 dozen, it's a good choice for a cookie exchange. Any leftover eggnog can be frozen.
 * Contributed by Catsrecipes Y-Group
 * About 10 dozen (2¼-inch) cookies

Cookies

 * 2 cups granulated sugar
 * 1 cup (2 sticks) unsalted butter, softened
 * 1 cup purchased eggnog
 * 1 teaspoon baking soda
 * ½ teaspoon ground nutmeg
 * 5½ cups all purpose flour

Glaze

 * 4 cups powdered sugar
 * 5 to 6 tablespoons purchased eggnog
 * 4 teaspoons dark rum or ¼ teaspoon rum extract
 * 1 teaspoon ground nutmeg

Cookies

 * 1) In large bowl, beat sugar and butter at medium speed until creamy.
 * 2) Beat in 1 cup eggnog, baking soda and nutmeg until blended.
 * 3) Gradually beat in flour until well blended.
 * 4) Cover and refrigerate 1 hour.
 * 5) Heat oven to 350°F.
 * 6) On lightly floured surface, roll out dough ¼ inch thick.
 * 7) Cut out with cookie cutters; place cookies on baking sheet.
 * 8) Bake 6 to 8 minutes or until lightly browned on bottom.
 * 9) Cool on wire racks.

Glaze

 * 1) Meanwhile, in medium bowl, whisk together all glaze ingredients until smooth.
 * 2) Spread glaze over cooled cookies.