How to Make It
Preheat the oven to 500°. Arrange the chicken in a roasting pan and roast until the skin is lightly browned, 20 minutes.
Transfer the chicken and any juices to a soup pot. Add the onions, carrot chunks, celery and herb sprigs. Add 4 quarts of water and bring to a boil. Simmer over moderate heat until the chicken is cooked, about 30 minutes. Using tongs, remove the chicken from the broth and let cool slightly.
Remove the meat from the bones and pull into shreds; discard the skin. Return the bones to the pot and simmer until the broth is reduced to 8 cups, about 1 1/2 hours. Strain the broth, discard the solids and skim off the fat. Season the broth with salt and keep warm.
Bring a large pot of salted water to a boil and fill a large bowl with cold water. Add the eggs and cook for 5 minutes. Using a slotted spoon, transfer the eggs to the bowl of cold water for 2 minutes. Crack the shells and peel the eggs.
Return the water to a boil and add the pasta. Cook until al dente. Drain and divide the pasta between 6 large soup bowls. Top with the shredded chicken, carrot matchsticks and soft-boiled eggs. Ladle the hot broth on top, garnish with basil leaves and serve, passing chile oil at the table.