In a small bowl, combine warm water, yeast, and 1 tablespoon of brown sugar. Allow the mixture to rest for 5 minutes until it becomes frothy.
In a large mixing bowl, combine the pumpkin puree, remaining brown sugar, pumpkin pie spice, and salt. Mix until well combined.
Add the yeast mixture to the pumpkin mixture and mix thoroughly.
Gradually add the flour, one cup at a time, while continuing to mix. The dough will become thick and sticky.
Transfer the dough onto a floured surface and knead it for approximately 5 minutes until it reaches a smooth and elastic consistency.
Coat a large bowl with vegetable oil, ensuring it is well-greased, and place the dough inside the bowl. Cover with plastic wrap and let it rise in a warm place for about 1 hour, or until the dough has doubled in size.
Line a baking sheet with parchment paper while preheating your oven to 425°F (220°C).
After the dough has risen, gently punch it down to release the air. Divide the dough into 8 equal-sized portions and shape each portion into a ball. Poke a hole in the center of each ball and stretch it to form a bagel shape.
Add water to a large pot and bring it to a boil. Add 1 tablespoon of brown sugar to the boiling water. Using a slotted spoon, carefully place 2-3 bagels at a time into the boiling water. Boil them for approximately 1 minute on each side.
Remove the bagels from the water using a slotted spoon and transfer them to the prepared baking sheet. If desired, sprinkle them with optional toppings such as pumpkin seeds or cinnamon sugar.
Place the bagels in the preheated oven and bake for 20-25 minutes, or until they achieve a beautiful golden brown color.
Once baked, transfer the bagels to a cooling rack and let them cool completely before serving.