Preheat oven to 350°F and spray baking sheets with nonstick spray. Combine flour, baking soda, baking powder, spices and salt in a medium bowl.
Beat sugar and butter in a large mixer bowl until well blended. Beat in pumpkin, egg and vanilla extract until smooth. Gradually beat in flour mixture. Drop by rounded tablespoon onto prepared baking sheets.
Bake for 15 minutes or until edges are firm. Cool on baking sheets for two minutes, then remove to wire racks to cool completely. For the glaze, combine powdered sugar, milk, melted butter, and vanilla in a small bowl until smooth; drizzle over cooled cookies.
If not serving cookies immediately, store unglazed in an airtight container at room temperature and glaze just before serving.
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