1/3 cup crushed hard peppermint candies, or more as needed
4 ounces unsalted butter, softened
4 ounces cream cheese, softened
2 cups powdered sugar
1 teaspoon vanilla extract
1 to 3 tablespoons eggnog
In a large bowl, beat together the butter and cream cheese with an electric mixer. With the mixer on low speed, add the powdered sugar a cup at a time until smooth and creamy. Beat in the vanilla extract and eggnog.
Warm frosting in microwave for about 15 seconds, spread onto cookies. Dip tops of frosted cookies into peppermints. Set cookies aside to let set.
Beat butter and confectioners' sugar in a bowl until creamy; stir vanilla extract into butter mixture. Gradually beat flour into mixture to make a smooth dough. Refrigerate until thoroughly chilled, 3 to 4 hours.
Preheat oven to 350 degrees F (175 degrees C).
Roll dough into 1-inch balls and place 2 inches apart on ungreased baking sheets.
Bake cookies in the preheated oven until lightly browned, 18 to 20 minutes. Remove to cool on wire racks.