Joint the chicken into eight pieces - legs, thighs, wings and breasts cut into two. Season with salt and fresh black pepper. Brown the chicken on both sides in a little olive oil in a frying pan and put in an ovenproof casserole.
Add a glass of white wine to the frying pan and reduce to half its volume or so scraping the bottom of the pan, and pour over the chicken. Pour chicken stock over the chicken to barely cover it. Add three or four stalks of tarragon, cover and cook in the oven at 300°F/150°C/Reg2 for a couple of hours.
Meanwhile top and tail the leeks, remove the outer leaves, cut into thinnish slices and put in a steamer. Scrape the baby potatoes, simmer in boiling water until just cooked, take out and drain, cut into half, and season with salt and black pepper. Chop some more tarragon to yield a couple of tablespoonfuls.
When the chicken is ready, start steaming the leeks until barely tender and sauteing the potatoes in a little olive oil. Take the chicken out of the casserole and keep warm, and discard the tarragon. Mix a tablespoonful of cornflour with a few tablespoonfuls of the cooking liquid, put into a saucepan and slowly stir in the remaining liquid over a medium heat stirring as you do so. Season with salt and pepper, add three tablespoonfuls of cream and the chopped tarragon and re-season if necessary.
Put a portion of leeks on to serving plates, add the chicken joints, spoon over some sauce and serve
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