Preheat oven to 400 degrees. Wrap sweet potato in foil, place on an oven-safe pan, and bake until tender, approximately 1 hour. Allow to cool slightly before peeling.
In a medium skillet, add oil and sauté onion over medium-low heat until tender, approximately 5 minutes. Add onion, sweet potato, and all other ingredients to the slow cooker, stir to combine. Cover and cook on low 6-8 hours, or high 3-4 hours.
Stovetop version: Follow the instructions above except add ingredients to a heavy pot, bring to a boil over medium-high heat, reduce heat to a simmer and cook until carrots are tender, approximately two hours. Add additional broth or water for a thinner soup consistency.