How to Make It
In a large pot, cover the chicken with 2 1/2 quarts of the water. Add the onion, carrot, cloves and a large pinch of salt and bring to a boil. Reduce the heat to low, skim the broth and simmer until the chicken is cooked through, about 1 hour and 15 minutes.
Transfer the chicken to a platter and let cool slightly. Skim the fat from the broth and measure 1 cup; reserve the remaining broth for another use. Remove the meat from the chicken and discard the skin and bones. Cut the chicken meat into bite-size pieces and transfer to a medium bowl.
In a shallow bowl, soak the bread in the remaining 1 cup of water until softened, then squeeze dry. In a food processor, combine 2 1/2 cups of the walnuts with the reserved 1 cup of broth, the bread, coriander, garlic, black pepper and 1 1/2 teaspoons of crushed red pepper; process to a coarse puree and add to the chicken. Finely grind the remaining 1/2 cup of walnuts in the food processor and stir into the chicken. Season the salad with salt and transfer to a serving bowl.
In a small saucepan, warm the walnut oil over low heat. Add the remaining 1 teaspoon of crushed red pepper and cook for 1 minute. Drizzle the hot oil over the chicken salad and serve at room temperature.