Place the bread in a bowl and pour the evaporated milk over it. Let it stand for 5 minutes, then mash it with a fork until very soft.
Heat the oil in a large skillet or Dutch oven over medium heat. Add the onion and cook, stirring often, until soft and translucent, about 5 to 7 minutes. Add the garlic and cook for 30 seconds, just until fragrant.
Transfer the softened bread mixture, cooked onion and garlic, ají amarillo paste, walnuts, and chicken broth to a blender. Blend until completely smooth. If using a standard blender, allow hot ingredients to cool briefly and vent the lid carefully according to the blender manufacturer's directions.
Return the blended sauce to the skillet over medium-low heat. Stir in the Parmesan, salt, and pepper. Cook gently, stirring frequently, until the sauce is hot, smooth, and lightly thickened, about 4 to 5 minutes. Do not let it boil hard.
Stir the shredded chicken into the sauce and cook until the chicken is heated through, about 4 to 5 minutes. If the sauce becomes too thick, stir in a splash of chicken broth or water. Taste and adjust the salt if needed.
Divide the cooked potatoes and rice among four plates. Spoon the creamy chicken stew over or alongside them. Garnish with egg halves, black olives, and parsley, if using. Serve hot.