In a large bowl, cream together softened butter, powdered sugar, and brown sugar until light and fluffy.
Add egg, vanilla extract, and almond extract (if using), mix well.
Add sourdough starter and mix until combined.
In a separate bowl, whisk together flour, baking powder, salt, and cream of tartar.
Gradually add dry ingredients to wet ingredients, mixing until just combined.
Dump out onto plastic wrap, wrap well and refrigerate for 8-24 hours.
Make the fermented crumble:
In a medium bowl, mix flour, brown sugar, salt, powdered sugar, cinnamon, nutmeg, ginger, and sourdough starter.
Add cold cubed butter and cut in using a pastry cutter or your fingers until mixture resembles coarse crumbs.
Add vanilla and mix gently.
Cover and refrigerate alongside the cookie dough for 8-24 hours.