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Preheat the oven to 475 degrees F. Dust a sheet tray with some flour.
In the bowl of a stand mixer fitted with the dough hook, combine the flour, brown sugar, salt, yeast, cinnamon, ginger and nutmeg. In a separate bowl, mix together the pumpkin, milk, molasses and eggs.
Add the pumpkin mixture to the dry ingredients and beat until just mixed. Add some water as necessary and mix until the dough forms a moist but not sticky ball.
Cut the dough into 4-ounce pieces, shape into bagels and place on the floured sheet tray. Let the bagels rise until they are about 50 percent larger, and soft and fluffy, 45 minutes to an hour. (The time will depend on the temperature and humidity in your kitchen.)
Meanwhile, bring a large pot of water to a boil, then reduce the heat to keep the pot at a simmer. Spray a sheet pan with nonstick cooking spray, top with parchment paper and spray with more spray. Gently place several bagels in the water and cook, allowing the water to return to a simmer, about 2 minutes.
Remove the bagels from the pot with a slotted spoon or spider and drain momentarily. Place on the prepared sheet pan. Stir together some cinnamon and granulated sugar and sprinkle over the bagels. Bake until slightly browned on top and firm to the touch, 30 minutes. Let cool 10 to 15 minutes, then remove from the pan so that they do not stick to the paper.