Rinse the chicken very well, carefully examining the carcass for any clumps of blood. Soak in a large bowl of salted water for 20 minutes; drain well.
Place the chicken in a large saucepan. Add the water, onion, carrot, parsley, bay leaf, and garlic. Heat, over medium heat, uncovered, until water is barely simmering. (For a nice, clear broth, the water should not be allowed to boil.) Cook chicken over low heat for at least 2 hours. Let cool slightly.
Line a sieve with a layer of dampened paper towel or a triple thickness of dampened cheesecloth. Set over a large bowl and carefully ladle the broth through the sieve. Discard all the vegetables except the carrot. Let the chicken cool until it can be handled without burning your fingers. Carefully pull the meat from the bones, discarding the skin, bones, and cartilage. Cut the carrot into slices and set aside with the chicken. (At this point the broth can be chilled and the fat lifted from the surface and discarded. The chicken meat and carrot can be covered and refrigerated until ready to use.)
Return the broth to the saucepan. Add the potato, chicken meat, and the carrot. Cook until potato is tender. Season to taste with salt. Meanwhile cook the pasta in a saucepan of boiling salted water until al dente, about 5 minutes; drain. Return to the saucepan and add a ladle of the hot broth to keep the pasta warm.
To serve, add a generous amount of pasta to each soup bowl. Add a ladleful of broth, some chicken, potato, and carrot slices. Serve piping hot with freshly ground pepper to taste, bananas, avocado and lime wedges.
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