Combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt; set aside
In a medium bowl, cream together 1/2 cup (1 stick) butter and white sugar. Add pumpkin, egg, and 1 teaspoon vanilla to butter mixture, and beat until smooth. Gradually beat in flour mixture. Drop on cookie sheet by tablespoonfuls; flatten slightly.
Bake for 15 to 20 minutes in the preheated oven, until the edges are slightly golden.
Allow them to cool on the baking sheet for 2 minutes and then transfer to a wire rack to cool completely.
Notes
This old-fashioned soft pumpkin cookie recipe literally melts in your mouth.