Preheat oven to 350° and grease baking sheets.
Combine flour, baking soda, baking powder, cinnamon, and salt in medium bowl. Beat sugar and butter in large mixing bowl until well blended. Mix in pumpkin, egg and vanilla extract until smooth. Gradually blend in flour mixture. Drop by rounded tablespoons onto prepared baking sheets.
Bake for 15 - 18 minutes or until edges are firm. Cool on baking sheets for two minutes then remove to wire racks to cool completely. Drizzle glaze over cookies.
Combine two cups sifted powdered sugar, 3 tablespoons milk, 1 tablespoon melted butter and 1 teaspoon vanilla extract and blend until smooth.
For a variation, chopped nuts may be added to the cookie batter.
Makes 3 dozen cookies.