Mix pumpkin puree and warm water, stir to combine. Add yeast, stir gently so yeast is submerged. Let sit 5-10 minutes until bubbly and frothy.
Combine dry ingredients in the bowl of a stand mixer with dough hook attached. Whisk to combine and evenly distribute the spices.
Make a well in the middle of the dry ingredients in the mixing bowl. Pour the yeast mixture into the center. Begin mixing with the dough hook on the lowest or second-lowest speed. If after 3-5 minutes, there is still lots of loose flour in the bowl, add warm water 1 TBSP at a time while the mixer is running, giving 30-45 seconds after each addition for the dough to absorb the water. Err on the side of less water — you're looking for a shaggy, messy dough.
Increase mixer speed to low-medium and knead for 3 minutes. You want a dough that is tacky and smooth, but not sticky. Dust in more flour as needed.
Shape the dough into a ball and place in a lightly greased bowl, turning once to coat. Let rest for 45-60 minutes, covered, in a warm spot. The dough should roughly double in size.
Punch the dough down and let rest an additional 10 minutes.
Divide the dough into eighths (using a kitchen scale for precision) and shape each piece into a ball.(How to shape a dough ball: Gently flatten the piece of dough against a lightly floured surface, then tuck the edges up into the middle, pinching them together to form a smooth surface on the underside of the dough. Then flip the dough over, cup your hand around it, pinkie against the counter, and drag your hand towards your body. Rotate the dough 90 degrees and repeat as needed.)Cover your shaped dough balls with a damp paper towel so they don’t dry out as you work. Divide the first dough ball you shaped in half, then roll each half into a rope approximately 10 inches long. Start with your hands in the middle of the rope, and move them outwards as you roll. If the dough resists, let it rest 3-5 minutes, then roll again. If the rope tears, pinch it back together and continue rolling with a slightly more gentle touch.IMPORTANT: DO NOT USE A FLOURED SURFACE. If you use a floured surface the ropes won’t stick together when you twist them and your bagels will fall apart.
Cross one rope over the other to form an “X” shape. Continue crossing the ropes over each other from the center outward until you have a twisted rope.
Bring one end of the rope over to meet the other so they overlap slightly. Squeeze gently to join them.Insert your hand into the center of the bagel with the joined ends on your palm. Gently but firmly press your palm down against the counter, rolling back and forth to seal the ropes together. Repeat with the rest of your dough balls, placing the shaped bagels back under a damp paper towel to rest while you make the others.Let the shaped bagels rest additional 10-15 minutes under a damp paper towel.
Preheat your oven to 425°F and bring a large, high-sided skillet filled with at least 3 inches of water to a boil.
Boil bagels 30-45 seconds per side (60 seconds max). If they stick to the bottom of the skillet, use a wire spider or slotted spoon to gently loosen them — the bagels should float. Place boiled bagels on a greased or silicone mat lined baking sheet.
Brush bagels with egg wash and dust with cinnamon sugar.If the joined ends of any of the wreaths come undone in the boiling water, use a wooden toothpick to hold the ends together in the oven while they bake.
Bake for 20 minutes at 425°F. Let bagels cool slightly on baking sheet, then transfer to wire rack to finish cooling. Remove any toothpicks before serving, duh.