Mix the dry ingredients. Stir together the flour, yeast, sugar, salt, cinnamon, ginger, and nutmeg.
Add the wet ingredients. Mix the sweet potato, vanilla, butter, and ½ cup lukewarm water. Add to the dry ingredients and stir until a stiff dough forms. If dry flour remains, add water 1 tablespoon at a time until it comes together.
Knead. Knead by hand for 10–12 minutes or with a dough hook on low for 6–8 minutes. Aim for a smooth, firm dough that is slightly tacky and holds its shape. Add a little flour if sticky, or a little water if too dry to knead.
First rise. Place in a lightly greased bowl, cover, and let rise for about 60–90 minutes, until puffy and nearly doubled. Judge by the dough’s appearance; it may need longer in a cool kitchen.
Shape. Gently press out the air and divide into 8 or 10 equal pieces. Roll into tight balls. Poke a hole through each center and stretch it to about 1½–2 inches wide.
Rest. Place on a parchment-lined baking sheet and cover loosely. Rest for 15–20 minutes, until slightly puffy. Meanwhile, preheat the oven to 425°F.
Boil. Bring a large pot of water and 1 tablespoon sugar to a gentle boil. Working in batches, boil the bagels for 30 seconds per side. Lift out, drain well, and return to the lined baking sheet.
Bake. Bake for 20–25 minutes, until golden brown and baked through. Start checking at 18 minutes because the sweet potato and sugar encourage browning.
Cool. Cool on a wire rack for at least 20 minutes before slicing.
Keep the dough firm: sweet potato varies in moisture, so add water gradually rather than pouring in extra all at once.