1. Bring chicken, next 7 ingredients, and water to cover to a boil in a Dutch oven over medium heat. Cover, reduce heat to medium-low, and simmer 1 hour.
2. Remove chicken, reserving broth in Dutch oven. Cool chicken 30 minutes.
3. Meanwhile, cook reserved broth in Dutch oven over low heat 30 minutes.
4. Skin, bone, and shred chicken, reserving bones. Place bones in broth. Cover and chill shredded chicken until ready to use.
5. Continue cooking broth, uncovered, over low heat 1 hour or until reduced by one-third. Pour broth through a wire-mesh strainer into a bowl; discard solids. Wipe Dutch oven clean; pour broth back into Dutch oven.
6. Skim fat from broth. Add thinly sliced onion and next 2 ingredients to broth; cook over medium-high heat, stirring occasionally, 20 minutes or until carrots are crisp-tender. Add shredded chicken; return to a simmer.
7. Add Sweet Potato Dumplings to soup. Garnish with Parmesan and parsley; serve immediately.