Pluck the leaves from the celery and place them in a stockpot. Chop off the carrot tops and peel the carrots, dropping both the peelings and tops into the pot. Chop off the root and top ends of the onion and peel it, tucking onion trimmings into the pot.

Mince the celery, carrots and onions very finely, and then place them in a mixing bowl.

Rinse the chicken thoroughly and pit it dry before adding it to the stockpot, covering it completely with water by about two inches.

Pierce the leeks with the cloves so that they remain stuck inside the tender stalks and place them in the stockpot alongside the stewing chicken.

Slowly simmer until the chicken is completely cooked and tender to the bone, about two hours. Carefully remove the chicken from the pot and place it on a platter to allow it to cool until you can pick the meat off the bones comfortably.

Strain the remaining broth through a fine-mesh sieve into a pitcher or jar, discarding the solids. Wipe the pot clean with a kitchen towel.

Melt the butter in a cast iron skillet until it foams, toss in the minced vegetables and fry until they become fragrant and tender, about 5 minutes. Transfer to the cleaned stockpot.

Once the chicken has cooled, pick its meat off the bones. Mince the meat very finely . Stir the chicken into the vegetables and pour the strained broth back into the stock pot. Stir in the finely grated nutmeg, and then bring it all to a bare simmer over medium heat.

Temper the beaten eggs by stirring a spoonful of broth into them, and then pouring the mixture of eggs and broth into the simmering soup. Gently stir in the heavy cream, parsley and chives. Season with salt and pepper.

Ladle into soup bowls and serve warm.