In a large bowl or electric stand mixer, combine the sourdough starter, buttermilk, melted butter, eggs, pumpkin puree, sugar cinnamon and other spices. Mix until smooth, then add the salt, flours and baking soda. Mix with a dough hook attachment for about 5 minutes (or knead by hand for 10 or more minutes), until the dough is smooth and elastic (but still rather sticky).
Cover the bowl loosely with a damp cotton towel or plastic wrap, and put it in a warm place to rise. After two hours, move the bowl to the refrigerator to continue slowly rising for 12-24 hours.
When ready to finish, prepare a floured surface. Take the dough out of the refrigerator and roll out to about 1/2 inch thickness. Use a donut cutter to form donuts; try to cut as many donuts as you can fit from the first slab, and gently tranfer each piece to a lightly floured parchment-lined tray. Gently reform the dough scraps into a ball and re-roll as needed to cut more donuts and donut holes.
After cutting donuts, lightly cover the tray with plastic wrap and move to a warm place to proof the donuts for about 25 minutes, until lightly plumped.
While proofing, heat a large dutch oven or other heavy-bottomed pan with oil over medium heat, until it reached 350 F.
After the donuts have finished proofing, very carefully transfer them into the hot oil, a few at a time to prevent crowding. When the first side is golden brown, flip the donuts and evenly brown the second side. Use a large slotted spoon or spider tool to lift donuts from the oil and move to a metal rack over a large sheet pan to drain.