Cover a piece of heavy cardboard with aluminum foil or freezer paper, dull-side up, to make a base for the gingerbread house.

Cut templates for the gingerbread house out of heavy cardboard or cardstock; label each piece.

Preheat oven to 350°F (175°C). Grease 3 rimless baking sheets (or the back of rimmed baking sheets).

Combine butter, brown sugar, molasses, dark corn syrup, lemon zest, cinnamon, nutmeg, ginger, salt, and mace in a large heavy saucepan over medium heat; stir until melted, about 5 minutes.

Sift flour into a large bowl. Stir into the butter mixture 2 cups at a time, mixing the last 2 cups by hand to create a warm, firm dough.

Roll out dough to 1/8-inch thickness on a greased baking sheet. Dust templates with flour and cut out shapes.

Bake pieces at 350°F until firm, 5-7 minutes for small pieces, 12-15 minutes for large pieces.

Cool on the baking sheet for 5-10 minutes, then transfer to a wire rack to cool completely for 15-30 minutes.

Combine confectioners' sugar, egg whites, cream of tartar, and white vinegar in a stand mixer for 7-10 minutes until the icing is shiny and stiff.