Preheat oven to 350°F. For the Cookies, mix flour, ginger, cinnamon, baking soda and salt in medium bowl. Set aside.
Beat butter, granulated sugar and molasses in large bowl with electric mixer on medium-high speed until light and fluffy. Add egg and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Drop by tablespoonfuls about 2 inches apart onto greased baking sheets, flattening slightly with palm of hand.
Bake 9 to 11 minutes or until lightly browned. Cool on baking sheets 2 minutes. Remove to wire racks; cool completely.
Meanwhile, for the Glaze, mix confectioners’ sugar, cream and lemon extract in small bowl with wire whisk until smooth. Drizzle over cooled cookies. Let stand 30 minutes or until glaze is set.