Combine flour, baking soda, baking powder, cinnamon, nutmeg and salt in medium bowl. Beat sugar and 1/2 cup (1 stick) butter in large mixer bowl until well blended. Beat in pumpkin, egg and 1 teaspoon vanilla extract until smooth. Gradually beat in flour mixture. Drop by rounded tablespoon onto prepared baking sheets.
Bake for 15 to 18 minutes or until edges are firm. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.
Combine sifted powdered sugar, milk, 1 tablespoon butter and remaining 1 teaspoon vanilla extract in small bowl until smooth. Drizzle over cookies.
