Beat the softened butter and granulated sugar together in a bowl until light. Add the egg and vanilla extract, then mix until combined.
Whisk the flour, baking powder, and salt in a separate bowl. Gradually add the dry mixture to the wet ingredients and stir until a dough forms.
Divide the dough in half, wrap each piece, and chill for 30 minutes.
Heat the oven to 350°F and line a baking sheet with parchment paper. Roll one piece of dough to 1/4-inch thickness on a lightly floured surface.
Cut out pumpkin shapes with a cookie cutter and place them on the baking sheet. Bake for 8 to 10 minutes until the edges are lightly golden. Cool completely on a wire rack.
Stir the powdered sugar and milk together to make icing. Divide the icing into two bowls and tint one orange and one black.
Spread orange icing over each cooled cookie. Pipe black icing to draw simple jack-o'-lantern faces.