Shred potatoes and carrots using the grating attachment of a food processor.

Bring chicken broth to a boil in a large pot. Boil shredded potatoes and carrots in the broth until soft, 5 to 10 minutes. Use an immersion blender to blend until smooth.

Heat a large skillet over medium-high heat. Cook and stir chorizo in the hot skillet until browned, 5 to 7 minutes. Transfer to a plate with a slotted spoon. Cook and stir onion in the chorizo grease until softened, about 5 minutes.

Pour blended broth into a slow cooker. Mix in chorizo and onion. Pour in pumpkin puree. Add brown sugar, butter, cinnamon, pepper, sage, rosemary, nutmeg, cloves, and thyme.

Simmer on High until flavors meld, about 1 hour.