In a wide pot, put 2-2.5 L of water, the chicken, the onion and the bay leaf; boil for 40 minutes, skimming off any foam as needed.
Remove the chicken and the onion from the pot.
Add the carrots, leek, celery and the olive oil; simmer over medium heat for 10 minutes.
Shred the chicken and put it back into the pot along with the thyme, nutmeg, and white pepper.
Add the trahanas, salt and pepper and, if necessary, extra hot water. When the trahanas is cooked, take the pot off the heat and let the soup cool slightly.
Ladle out 1 cup of the hot broth (so that it cools) to make the avgolemono.
In a bowl whisk the two eggs, then slowly pour in the cooled broth and the lemon juice.
Pour the egg-lemon mixture back into the pot, stir and serve.
