In a large kettle or stockpot combine the carcass with 4 1/2 quarts of the water, or enough to cover it, and simmer, uncovered, for 3 hours. Strain the stock through a large sieve into a large bowl, return it to the kettle, and boil it until it is reduced to about 10 cups.
In a blender puree the garlic and the gingerroot with the remaining 1/3 cup water. In a heavy kettle heat the oil over moderately high heat until it is hot but not smoking and in it cook the puree, stirring, for 2 minutes, or until the liquid is evaporated. Add the curry powder and the cumin and cook the mixture, stirring, for 1 minute. Add the potatoes, peeled and cut into cubes, onion, carrots, and 5 cups of the stock and simmer the mixture, covered, for 30 minutes, or until the vegetables are very soft. In the blender puree the mixture in batches until it is smooth, transferring it as it is pureed to another large kettle. Stir in the remaining stock, coconut milk, lime juice, and salt to taste, simmer the soup for 10 minutes, and stir in the chopped coriander.
The soup may be made 2 days in advance, cooled completely, uncovered, and kept covered and chilled. The soup keeps, covered and frozen, for 2 months. Serve the soup garnished with the coriander sprigs.