Mix the flour, ginger, cinnamon, baking soda, and salt in a bowl. Set the bowl aside.

Beat the butter and brown sugar until smooth. Add the molasses and egg, then mix until combined. Slowly add the dry mixture and stir until a dough forms. Wrap the dough and chill it for 30 minutes.

Heat the oven to 350 degrees. Roll the dough to 1/4-inch thickness on a lightly floured surface. Cut four house shapes with a knife or house-shaped cutter and place them on a baking sheet. Bake for 10 minutes. Let the cookies cool completely on the sheet.

Stir the powdered sugar and milk together until smooth. Add black gel food coloring until the icing reaches a deep black shade. Spoon the icing into a piping bag and pipe outlines of windows, doors, and roof lines on each cookie. Press green candy melts along the roof edges and add mini chocolate chips for extra detail. Let the icing set before serving.