Mix together flour, cornstarch and salt in a medium bowl and set aside. Cream together butter and 1/4 cup powdered sugar. Beat in the eggnog. Add flour mixture gradually until well blended. Cover and refrigerate for an hour, or until the dough is firm.
Preheat oven to 350 degrees and line 2 cookie sheets with parchment paper. Roll dough into 1-inch balls and place on baking sheet 1-inch apart. Bake 12-14 minutes, than roll in powdered sugar. Makes about 3 dozen cookies.