Season the duck heart and gizzard with salt and pepper and cook them slowly in the duck fat over low heat until very tender, about 30 minutes. They should not brown. Remove them from the fat and cut into thin strips.
Heat the duck stock and add the lemongrass and ginger. Simmer for 5 minutes and then add the rest of the ingredients, including the heart and gizzard. Simmer for another 2 minutes, season to taste, and ladle into 4 warm bowls.
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