Using the tip of a sharp knife, scrape pulp from vanilla bean; set aside. In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, nutmeg, and salt. Beat until combined, scraping bowl occasionally. Beat in egg, eggnog, and vanilla pulp or vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Divide dough in half. Cover and chill 1 hour or until dough is easy to handle.

Preheat oven to 375 degrees F. On a lightly floured surface, roll out one of the dough portions to 1/4 inch thick. Using a fluted round 3-inch cookie cutter, cut out dough. Place dough rounds 1 inch apart on an ungreased cookie sheet. Bake in the preheated oven for 8 to 10 minutes or until edges are firm and bottoms are just lightly browned. Transfer cookies to a wire rack; let cool. Repeat with other dough portion. Spread cookies with Eggnog Icing. If desired, sprinkle with coarse sugar. Let icing dry. Makes about 24 cookies.

In a medium bowl, stir together 3 cups powdered sugar and 1/2 teaspoon vanilla. Stir in enough dairy or canned eggnog or milk (3 to 4 tablespoons) to make an icing of spreading consistency.

Layer cookies between sheets of waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.