This soup with lots of shredded kale makes great use of leftover turkey. If you've already frozen the carcass, there's no need to thaw it out before using it in this recipe.
Place the carcass in a large soup pot or stockpot and add cold water to cover by 2 inches (about 14 cups). Bring to a boil over high heat, skimming any foam that rises to the surface.
Add carrots, celery, tomato paste, 1 teaspoon salt, and 1/2 teaspoon rosemary. Return to a boil; reduce to a simmer and cook until the broth is rich and flavorful, about 2 hours.
With a wire skimmer, remove and discard turkey carcass and vegetables. Strain and transfer 8 cups of broth to a large saucepan; freeze the remainder.
Bring broth to a boil over high heat. Add red-pepper flakes and remaining 1/2 teaspoon rosemary; season with salt. Add kale, reduce to a simmer, and cook until kale is tender, 5 to 7 minutes.
Stir in turkey, corn, beans, and scallions and cook just until corn is heated through, about 2 minutes. Season with salt, if desired.