Heat the oven to 350 degrees and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, ginger, and salt.
In a large bowl, beat the butter and granulated sugar until light. Add the egg and pumpkin puree and mix until smooth.
Stir the dry ingredients into the wet ingredients until a soft dough forms. Cover and chill the dough for 20 minutes.
Roll the dough to 1/4-inch thickness on a lightly floured surface. Cut into shapes with cookie cutters and place on the baking sheet.
Bake for 10 to 12 minutes until the edges are lightly golden. Cool the cookies completely on a wire rack.
In a small bowl, stir the powdered sugar, orange juice, and orange zest until smooth. Drizzle or spread the glaze over the cooled cookies.