In a medium-sized saucepan, melt the butter, corn syrup, molasses, and brown sugar over medium-low heat, stirring until sugar is dissolved. Set aside, and allow to cool.
In a large mixing bowl, whisk together the flour, pumpkin pie spice, ground ginger, baking soda, and salt.
Pour the syrup into the dry ingredients, and mix well until a dough forms. (The dough will stick together well, but should not be sticky or too loose.)
Divide the dough among the molds, and press into an even layer.
Bake for 35 to 40 minutes, until firm.
Remove from baking sheet to a cooling rack, and cool completely, 1 to 2 hours.
Once it is completely cooled and hardened, carefully peel the gingerbread pieces away from the molds.
Add egg whites and cream of tartar to a stand mixer, and beat on medium-high until soft peaks form.
Gradually add in the powdered sugar while mixing on low.
Increase the speed to medium-high, and beat for about 2 minutes until fluffy and well-combined.
Put icing in a piping bag with a round tip.
Cover any extra icing with plastic wrap — touching the icing so that it doesn't form a crust — as it will dry quickly.
Identify the back of the house, and make a thick strip of icing along the bottom. Place on your chosen smooth surface, and prop up with heavy items like food cans to let the icing dry.
After the back of the house, place the sides on with thick strips of icing along the bottoms and sides.
Place the front of the house on with thick strips of icing along the bottom and sides.
Place on the roof pieces, using plenty of icing to cement it all together.
Add the door and the other figurines.
Use the leftover icing to decorate the house with candy, make icicles, a snowy roof, and/or a snowy lawn. (Decorate shortly after piping on the icing — the icing dries quickly, and the candy pieces won't stick to icing that's been sitting out for a while.)