Beat sugar and butter together in a bowl using an electric mixer until smooth and creamy; beat in egg until smooth. Mix pumpkin and vanilla extract into creamed butter mixture; add cinnamon, salt, and baking powder. Stir flour into pumpkin-butter mixture just until dough is mixed. Refrigerate dough, 2 hours to overnight.
Preheat oven to 400 degrees F (200 degrees C).
Roll dough on a floured work surface and cut into shapes using cookie cutters. Arrange cookies on a baking sheet.
Bake in the preheated oven until edges are lightly browned, 6 to 8 minutes.
