Combine flour, sugar and gingerbread spices. Add butter and use a pastry cutter to combine. Add cream and knead quickly to form a pastry. Wrap in foil and refrigerate 45 minutes.
Preheat the oven to 180°C (approximately 350°F). Roll out dough on a lightly floured surface to about 5 mm (approximately 1/5 inch). Cut 30 rectangles (about 5 x 4 cm OR 2 x 1 1/2 inches) and place on a baking sheet lined with parchment paper. Bake until golden brown, about 10 minutes. Remove and let cool on a wire rack.
Melt couverture in a double boiler and pour into a small piping bag with a very small tip. Pipe a diamond-shaped grid onto 20 cookies and let dry.
Whisk egg, add icing sugar and stir until creamy. Pour into a piping bag with a medium tip.
To build the house: Decorate the edges of the 20 cookies that have couverture, as desired, with egg white glaze. Allow to dry. Take a marshmallow and attach two cookies (with the couverture) to the top, using the egg mixture, to form a roof. Allow to dry. Use remaining 10 cookies to form the base of the house. Attach base with egg white mixture to the bottom of the marshmallow. Allow to dry. Use remaining egg white mixture to decorate, as desired. Allow to dry completely and serve.