In a non-stick pan, coated with a thin film of olive oil, cook the brunoise celery over medium heat until caramelized.
Transfer to a stainless steel bowl, and set in an ice bath to cool.
In a large mixing bowl, combine the chicken, onions, carrots, cooled celery, and the leeks with 2 egg whites and mix well.
In a large pot, combine the chilled stocks. Add a small amount of the stock to the chicken mixture. Add the tarragon, parsley, peppercorns, bay leaves, and thyme and mix well.
Transfer the chicken mixture to the stockpot. Heat, stirring occasionally, until the chicken mixture forms a raft on top of the stock; do not stir after raft has formed. Simmer on very low heat for 20 minutes.
Strain through cheesecloth and return to the stockpot. Reheat, removing excess fat with absorbent paper.
Blanch the celery and potato paysanne in boiling salted water, until crisp-tender. Shock in ice water and drain well. When ready to serve, place the paysanne vegetables, in 4 heated bowls. Carefully ladle 4 to 6 ounces of the celery essence into the bowls.