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 the heat to a low boil and poach the chicken for 15 minutes. Remove the chicken and shred or slice. Strain the stock.
Meanwhile, in another deep skillet, heat the butter an EVOO over medium heat. Add the leeks and cook until softened, 6 to 7 minutes. Season with salt and pepper, sprinkle with the flour and stir for a minutes. Add the wine and ladle in 1 cup of the chicken poaching stock. Stir in the cream for about 5 minutes to thicken. Stir in the tarragon and mustard. Add the chicken.
Align the toast triangles on plates point to point, with the cut sides facing out. Top with the cream of chicken and leeks.