Preheat oven to 350 degrees F. Grease cookie sheets.
Combine flour, baking soda, baking powder, cinnamon, nutmeg, and salt in medium bowl. Set aside.
Cream butter and sugar in mixer bowl.
Add pumpkin, egg and vanilla to butter mixture; beat until light and creamy.
Add dry ingredients into butter mixture; mix until well blended.
Drop mixture by round tablespoon onto cookie sheet; smooth top of cookies.
Bake 15-20 minutes. Cool on wire rack.
To make the glaze, mix confectioner's sugar, milk, butter, and vanilla until smooth. Drizzle over top of cookies.
For a true 'scratch' pumpkin cookie, roast a small 'sugar pie' pumpkin or butternut squash: preheat oven to 400 degrees F. Using a serrated knife, carefully cut off stem of squash or pumpkin bottom; carefully slice in half from stem to bottom (do not peel skin). Remove seeds and lightly oil cut side and cavity. Place cut-side-up on baking dish or cookie sheet and bake until a fork can easily pierce through flesh, about 40 minutes and up to 1 1/2 hours depending on size. You may need to turn pumpkin over halfway through baking. Puree well and measure the same as canned. Cool to room temperature before refrigerating in an airtight container. Keeps up to 1 week or freeze up to 1 month.