Preheat oven to 400 degrees F (200 degrees C).

Beat butter and sugar with an electric mixer in a large bowl until smooth and creamy, about 2 minutes. Mix in canned pumpkin, egg, cinnamon, vanilla, nutmeg, pumpkin pie spice, and ground ginger until well combined.

Stir flour and baking powder together in a small bowl. Add flour mixture to pumpkin mixture in thirds, mixing dough well between each addition.

Spoon cookie dough into a cookie press fitted with a pumpkin-shaped die and press dough onto a baking sheet.

Bake in preheated oven until edges just begin to brown, about 8 minutes. Cool cookies on baking sheet for 5 minutes before transferring to a wire rack.