Place the chicken in a deep skillet and season with salt. Add the carrot, celery, onion, lemon, bay leaf, thyme, parsley and just enough water to cover the chicken. Bring to a boil then lower heat to a low boil and poach chicken for 15 minutes. Remove the chicken and shred or slice. Strain the stock.
Meanwhile, in another deep skillet, heat butter and EVOO over medium heat. Add the leeks and cook until softened, about 6-7 minutes. Season with salt and pepper; sprinkle with flour and stir for a minute. Add the white wine and ladle in 1 cup of chicken poaching stock. Stir in the cream for about 5 minutes to thicken. Stir in the tarragon and mustard. Add the shredded or sliced chicken.