Preheat the oven to 350°F. Line a 12-cup muffin pan with liners or in a silicone muffin pan.
In a mixing bowl, whisk together flour, baking powder, baking soda, salt, and pumpkin pie spice.
In a separate mixing bowl, combine pumpkin puree, sourdough starter, cooled melted butter or oil, maple syrup or honey, egg, and vanilla. Stir until smooth.
Add the dry ingredients to the wet ingredients and gently stir until just combined. Do not overmix.
Fold in chocolate chips, nuts, or berries if desired.
Divide batter evenly between muffin cups, filling each about 3/4 full.
Bake for 20–23 minutes, or until lightly golden and a toothpick inserted in the center comes out clean.
Let muffins cool for several minutes before transferring to a cooling rack.