In the bowl of a stand mixer fitted with the paddle attachment, cream together the softened butter, white sugar, and dark brown sugar until light and fluffy.
Add the egg, vanilla extract, blackstrap molasses, and sourdough starter. Mix until well combined.
In a separate bowl, whisk together the flour, ground ginger, pumpkin pie spice, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a firm dough forms. If the dough feels sticky, add up to 2 tablespoons more flour for a rollable consistency.
Wrap the dough tightly in plastic wrap and refrigerate for at least 2 hours, or up to 48 hours for deeper flavor and better texture.
On a lightly floured surface or between pieces of parchment paper, roll the dough to ¼ inch thick.
Use cookie cutters or your gingerbread house template to cut out shapes. Transfer to a prepared baking sheet.
Bake at 350°F (175°C) for 10–12 minutes for a firm but slightly chewy texture, or 13–15 minutes for crispier cookies.
Cool completely on a wire rack before decorating with royal icing or assembling your gingerbread house.