In a bowl, combine the flour, ginger, baking soda, cinnamon, nutmeg and salt. Set aside.
In another bowl, cream the butter, brown sugar and molasses with an electric mixer for about 2 minutes. Add the egg and stir well. At low speed or with a wooden spoon, stir in the dry ingredients until smooth.
Shape the dough into 2 discs. Cover with plastic wrap and refrigerate for 1 hour.
With the rack in the middle position, preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.
On a lightly floured surface, knead the dough with your hands for about 1 minute. Roll out to an 1/8-inch (3 mm) thick sheet. Cut out cookies using the cookie cutters. Reuse any dough scraps. Place the same size cookies on the same baking sheet.
Bake one sheet at a time for about 10 minutes or until the cookies are lightly browned. Let cool completely.
In a bowl, whisk the egg white and icing sugar with an electric mixer until smooth.
With a pastry bag filled with the icing and fitted with a small plain tip, pipe icing on the edges of the house pieces and assemble it.