Whisk together until smooth the egg whites and 1 1/3 cups of the powdered sugar.
If you are planning to eat your gingerbread house, and are concerned about the safety of raw eggs, you can microwave the egg white powdered sugar mixture for several seconds (30-40) until the mixture reaches a temperature of 160 degrees, but not higher than 175°F. You can also use pasteurized dried or liquid egg whites.
Add the remaining 1 1/3 cup of powdered sugar to the sugar egg mixture. Using an electric mixer, beat on high speed until the icing holds stiff peaks. If it doesn't form stiff peaks, add more powdered sugar.
Place a dampened clean towel over the bowl of royal icing. Keep this towel over the icing to prevent it from drying out while you work with it.
When you are ready to mortar or decorate, fill a pastry bag with the icing. If you don't have a pastry bag, you can make your own with a re-sealable plastic freezer bag, just cut off the tip (a small cut) of one of the corners of the bag. Plastic or metal piping tips are available in supermarkets which you can also use with a freezer bag, for more controlled piping.