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For the Cookies, mix flour, baking soda, cinnamon, nutmeg and salt in medium bowl. Set aside. Beat granulated sugar and butter in large bowl with electric mixer on medium speed until light and fluffy. Add egg and 2 teaspoons vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Refrigerate 2 hours or overnight until firm.
Preheat oven to 375°F. Roll out dough on lightly floured surface to 1/8-inch thickness. Cut into shapes with favorite cookie cutters. Place on greased baking sheets.
Bake 8 to 10 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.
For the Glaze, mix confectioners' sugar, milk and 1/4 teaspoon vanilla in small bowl until smooth. Stir in corn syrup until glaze is smooth and glossy. (If glaze is too thick, stir in small amount of additional corn syrup.) Stir in 3 to 4 drops food color until evenly distributed and glaze is smooth. Add additional drops of food color until glaze is of desired color. To glaze cookies, hold a cookie by its edge and dip the top into the glaze. (Or spoon the glaze onto cookies using a teaspoon.) Place glazed cookies on wire rack to dry.