Combine turkey carcass, halved onion, roughly chopped carrot, roughly chopped celery, halved garlic head, 1 teaspoon rosemary, thyme, bay leaves, salt and pepper in a stock pot; pour in enough water to cover. Bring mixture to the boil; cover pot, reduce heat and simmer until flavours have blended, about 1 hour.
Remove turkey carcass and pull remaining meat from bones; reserve meat and discard carcass. Remove vegetables and bay leaves from stock using a slotted spoon and discard.
Stir diced onions, diced carrots, diced celery, minced garlic, Italian herb seasoning, 1 teaspoon rosemary, and onion granules into stock; bring to the boil. Reduce heat, cover pot and simmer until vegetables are very tender, 20 to 30 minutes. Add cooked rice and turkey meat to soup; season with salt and pepper. Cook until rice and turkey have warmed through, about 5 minutes.