Start by drying the whole chicken with paper towels. Wet skin doesn't brown well, so drying it is important. Heat some olive oil in a large Dutch oven over medium-high heat. Place the chicken in the pot. Brown it on all sides until the skin is a deep golden color, which takes about 10 minutes. Take the chicken out and set it on a plate.

While the chicken is browning, slice the leeks and rinse them in cold water to remove any sand. Chop the fennel, carrots, and celery into similar-sized pieces so they cook evenly.

In the same pot used for the chicken, add the leeks, fennel, carrots, and celery. Cook over medium heat for about 10 minutes, stirring often, until the vegetables are soft and fragrant.

Place the browned chicken back into the pot on top of the vegetables. Sprinkle saffron, salt, and pepper on top. Pour in chicken stock and water until the chicken is mostly covered.

Tie the thyme sprigs and bay leaf together with kitchen string and add the bundle to the pot. Cover the pot with a lid and put it in an oven set to 350°F. Bake for about 1 hour and 15 minutes, until the chicken is fully tender.

Take the pot out of the oven and move the chicken to a cutting board to cool slightly. Stir the orzo into the hot broth, cover the pot again, and let it rest off the heat for 20 minutes. The orzo will cook during this resting time using the residual heat.

Remove the herb bundle from the pot. Tear the chicken meat off the bones into large pieces, then discard the skin and bones. Stir the meat back into the soup. Add lemon juice and taste the broth to adjust the salt and pepper. Serve the soup in bowls and garnish with fresh dill or parsley.