In a large bowl, combine the water, brown sugar, and yeast. Let sit 5-10 minutes until the yeast bubbles and becomes foamy.
Whisk in the sweet potato puree. Using the dough hook attachment on your mixer, add in 3 cups of the flour, the cinnamon, ginger, cloves, and salt. Knead until a soft, tacky, but firm dough forms, about 5-10 minutes. Add 1 tablespoon of flour at a time, as needed, if the dough is too sticky.
If kneading by hand, turn the ball of dough onto a floured surface and knead 10-15 minutes, adding flour as needed until the desired texture is reached.
Grease a clean bowl and toss in the dough ball, flipping to coat both sides lightly with oil. Cover with plastic wrap or a tea towel and let rise in a warm, draft-free area until doubled, about an hour.
Preheat oven to 450 degrees. Line two large baking sheets with parchment.
Punch down the dough and divide in half, then divide each half into four roughly equal-sized balls. You will have 8 balls, then. That's a lot of balls. Roll into a neat little sphere and poke a thumb into the center, then stretch the ball into a doughnut shape with the center hole around 1 inch in diameter. Lay onto the baking sheet. Repeat with the remaining dough balls. Cover and let rest 10 minutes.
Bring a large pot of water to a simmer. Stir in the baking soda. Drop 2 bagels into the water and simmer for 30 seconds. With a slotted spoon, flip and simmer 30 more seconds. Remove the bagels from the water and set on the baking sheets. Repeat with remaining bagels.
Dab any excess moisture off the bagels and the parchment. Bake for 12-15 minutes until lightly golden and puffy. Transfer to a wire rack and let cool.