Combine flour, baking soda, salt, cinnamon, and ground ginger in a large mixing bowl. Whisk them together well and set the bowl aside.
In another bowl, blend sourdough starter, melted butter, brown sugar, granulated sugar, molasses, and egg and mix well until creamy.
Pour wet mix and dry and combine thoroughly using stiff spatula or spoon. Dough will be stiff, so you may need to use your hands to finish making sure it is well mixed.
Cover in plastic wrap and refrigerate for at least a few hours or up to 4 days for long fermentation.
Preheat oven to 350°F.
When dough is ready, place onto lightly floured surface and roll until ¼ inch thick. You may need to flatten out with your hands a bit first if dough is too stiff.
Use a small jar, cup, or cookie cutters to cut shapes into dough.
Carefully place cookies on a tray lined with parchment paper giving enough space for cookies to expand.
Use leftover dough cuttings by squishing thoroughly together and re-rolling to ¼ inch thickness and use cutters until remaining dough is all used up.
Bake for 8-10 minutes.
Cool completely before icing or decorating