Place the chicken in a large saucepan. Add the halved carrot, the halved onion, the whole black peppercorns, the sprig of parsley, the sprig of thyme, the chicken stock and the white wine and bring up to the boil. Season with salt and freshly ground black pepper, cover with the lid and place in the preheated oven to cook for 1½-2 hours, or until the chicken is completely cooked. I test for this by pulling the leg - if it feels as though it will come away from the carcass easily and the juices run clear when it is pierced, then the chicken is ready. (For a large chicken, cook for 20 minutes per 450g (1lb) plus 30 minutes).
Remove the chicken from the stock and put it on a large plate. Remove all the meat from the carcass, discarding the skin and bones. Cut the chicken meat into strips, roughly 1cm x 5cm (½in x 2in). Cover and keep warm.
Strain the stock to remove the vegetables, peppercorns and herbs and discard them. Return the stock to the saucepan, add the cream, bring the liquid up to the boil and boil, uncovered, for a few minutes to reduce the liquid. Season to taste. As the sauce is cooking, make the roux. Melt the butter in a small saucepan on a medium heat, add the plain flour and allow to cook for two minutes, stirring regularly, until it is a pale golden colour, then set aside.
While the sauce is still boiling, whisk in about half of the roux. You need enough to thicken the sauce, so it just coats the back of a spoon. If it is too thin, whisk in more of the roux. Put the chicken and juices back in the saucepan, taste for seasoning, adjusting if necessary, and keep warm until needed.
Serve with mashed or boiled new potatoes and a green salad.