Heat the oven to 350 degrees and line a baking sheet with parchment paper.
Stir the flour, baking powder, salt, and pumpkin pie spice together in a bowl.
In a second bowl, beat the butter and granulated sugar until smooth. Add the pumpkin puree, egg, and vanilla extract and mix well.
Combine the wet and dry mixtures until a soft dough forms. Scoop rounded tablespoons of dough onto the baking sheet and flatten each slightly.
Bake for 10 to 12 minutes until the edges are lightly golden. Let the cookies cool on the sheet for a few minutes before moving them to a rack.
Mix the powdered sugar and milk in a small bowl until the icing is smooth but thick enough to hold its shape.
Spread the icing over the cooled cookies and press two mini chocolate chips into each one to make ghost eyes.