Place warm water in a large bowl and add yeast and brown sugar. Stir and let sit for about 3-5 minutes. 

Add in pumpkin, spices, salt, and 2 cups of bread flour and begin to stir together to form a soft, sticky dough.

Transfer the sticky dough to a lightly floured surface and add in another cup of flour and begin to knead dough by hand until all of the flour is absorbed. Add in another 1/2 cup of flour and knead again until all of the dough is absorbed. Knead dough for about 8 minutes. The dough should not be sticky, but smooth and elastic.

Place dough in a bowl coated with oil, and cover the top allowing it to rise in a warm place until dough doubles in size, about 1 hour.

After an hour, punch down the dough and shape into 12 balls. 

Shape your bagels: roll each dough ball into a rope, about 8 inches long. Wrap the dough around to form a complete circle and overlap the dough. Seal the two ends together completely by rolling a bit; this is an important step or the ends will come apart when you boil them. Alternatively you can push your thumb through the center to form a 2 inch hole and stretch the dough to form an even ring. 

Place the bagels on a baking sheet (greased or lined with parchment paper), cover again with plastic wrap and let rise for 15-20 minutes more.

Preheat oven to 400 degrees F. Coat baking sheet with cooking spray.

Fill a Dutch oven two-thirds full with water and bring to a boil. Drop bagels, two at a time, into boiling water. Cook for about 45 seconds on each side. 

Remove with a slotted spoon; drain well on paper towels. Place on baking sheets, brush with egg wash, and bake for 15-20 minutes or until golden brown. Remove and cool on wire racks.

Spread on toasted bagels and enjoy!