Preheat the oven to 350 degrees and line a baking sheet with parchment paper.
Whisk together the flour, ground ginger, cinnamon, baking soda, and salt in a medium bowl.
In a separate bowl, beat the softened butter and brown sugar until light. Add the molasses and egg and mix until smooth.
Stir the dry ingredients into the wet mixture until a dough forms.
Roll the dough to 1/4-inch thickness on a lightly floured surface and cut into Halloween shapes.
Place the shapes on the prepared baking sheet and bake for 8 to 10 minutes until the edges are firm. Let the cookies cool completely on the sheet.
Mix the powdered sugar and milk into a smooth icing. Divide the icing and tint portions black and orange with the food coloring.
Pipe the colored icing onto the cooled cookies to create haunted faces and details.