1. Put the turkey carcass, broth, garlic, bay leaves and thyme in a large Dutch oven (cut carcass in pieces if necessary so it fits) and add enough water to cover by an inch. Bring to a boil over medium-high heat; lower heat and simmer, uncovered, about 40 minutes. Strain the soup through a fine-mesh strainer into a large bowl; discard the solids. Add all but 2 cups of the broth back to the Dutch oven; reserve the remaining broth for another use (it will keep refrigerated up to 3 days or frozen up to 1 month).
2. Add the turkey meat, green beans, corn and sweet potatoes to the pot; cover and cook over medium heat for 15 minutes. Add the pasta and continue to cook, uncovered, until the pasta and potatoes are tender, 10 to 12 minutes. Stir in the dill and pepper and season to taste with salt. Serve with the bread.
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