In the bowl of a stand mixer, combine the active sourdough starter, pumpkin puree, water, honey, and pumpkin pie spice. Mix until combined. Add the flour and salt and knead on medium speed for 7 to 8 minutes, until the dough is smooth and pulls away from the sides of the bowl.

Transfer the dough to a lightly oiled bowl and cover. Let it rise at room temperature for 6 to 8 hours, or until doubled in size.

Turn the dough onto a lightly floured surface and divide into 12 equal pieces. Shape each piece into a smooth ball. Poke your thumb through the center of each ball, then gently stretch the opening to form a bagel.

Place the shaped bagels on a parchment lined baking sheet, cover, and let rest for 30 minutes.

For a stronger sourdough flavor, cover the shaped bagels and refrigerate overnight. They can be boiled and baked straight from the refrigerator the next morning.

Bring a large pot of water to a gentle boil and add 1 tablespoon baking soda. Working with 1 to 2 bagels at a time, boil for 30 to 40 seconds per side for a softer texture, or up to 1 minute per side for a chewier bagel. Remove with a slotted spoon and return to the parchment lined baking sheet.

Preheat the oven to 425°F. Bake on the middle rack for 20 to 25 minutes, or until golden brown.

Transfer the bagels to a cooling rack and let cool for at least 30 minutes before slicing.