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Mix flour, baking soda, cinnamon, ginger and allspice in large bowl. Beat butter, 1/2 cup of the granulated sugar and brown sugar in large bowl with electric mixer on medium speed until light and fluffy. Add molasses; mix until well blended. Add egg and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Cover. Refrigerate 30 minutes or until firm.
Preheat oven to 350°F. Shape dough into 1-inch balls. Roll in remaining 1/2 cup granulated sugar. Place 2 inches apart on ungreased baking sheets.
Bake 12 to 15 minutes or until cookies are set. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.