First, place the chicken in a large, deep pot and add the carrot, celery, and onion. Cover with about 3 liters of water, making sure the chicken is fully submerged. Bring to a boil. Skim off any foam that forms on the surface during the first few minutes of boiling, using a ladle.

Lower the heat, cover the pot, and simmer until the chicken is tender, about 1 hour and 15 minutes. Season with salt and pepper. Remove the chicken and place it on a platter, keeping it warm and covered.

Strain the broth and discard the vegetables. Return the broth to the pot and add the pasta. Cook for a few minutes until the pasta is done. Remove the pot from the heat to stop the boiling and let it rest for a few minutes.

Dissolve the cornstarch in the lemon juice. In a bowl, whisk the eggs (starting with the whites), then gradually add the lemon juice while continuing to whisk. Slowly temper the avgolemono by adding a bit of hot soup from the pot, always whisking to balance the temperature of the eggs.

Meanwhile, debone the chicken.

Pour the avgolemono mixture into the soup, stirring gently to combine. Cook on very low heat for about a minute until it slightly thickens, stirring regularly. Season again with salt and pepper if needed.

Serve the chicken soup in warm bowls, adding some chopped chicken to each bowl, along with extra lemon, carrot, and a sprinkle of salt and pepper.