Mix pumpkin puree, milk and sourdough starter together in a bowl.
In another bowl, beat the butter (or oil) and sugar together until light and fluffy. Add in the vanilla extract and eggs and mix until well combined.
Add the pumpkin puree mixture to the butter and sugar mixture and mix until all incorporated.
Add the baking powder, baking soda, pumpkin pie spice and mix well. Slowly add in the flour and mix until just combined, without overtaxing. For a long ferment, cover well and refrigerate for 1-3 days.
Preheat oven to 350°. Pour batter onto an oiled or parchment paper lined baking sheet and bake for 20-30 minutes or until a toothpick comes out clean. Let cool before frosting.*This is a very lightly sweetened bar. For a sweeter pumpkin bar, add 1 cup of sugar.