To make spiced molasses cookies, preheat the oven to 350°F and line a cookie sheet. Beat butter until smooth, add 1 cup sugar, egg, and molasses, then mix well.
In a separate bowl, whisk flour, baking soda, cinnamon, ginger, and cloves, gradually add to wet ingredients and mix thoroughly. Drop scoops of dough into sugar, coat, and place on the cookie sheet.
Bake for 12-14 minutes, cool on the pan before transferring to a rack. For the drizzle, mix powdered sugar, eggnog, and nutmeg, adjusting consistency as needed.
Pour the glaze into a zip-top bag, cut a small opening, and drizzle over cooled cookies. Allow the glaze to harden, then store the cookies in an airtight container.