Melt the butter and lightly brown the chicken all over in a cast-iron casserole. Season lightly with salt and pepper. Add the wine, the bouquet garni and sufficient water to cover the first joint of your finger. Bring to the boil.
Cover tightly and turn down the heat. Simmer gently for 45–60 minutes until the chicken is cooked.
Lift out the chicken, joint it and arrange the pieces on a hot oven dish; keep hot while you make the sauce. Remove any surplus fat from on top of the cooking liquid by floating a sheet of kitchen paper on the liquid to absorb the fat.
Remove the bouquet garni and add the beurre manié in small pieces, whisking over medium heat until the sauce has thickened. Add the cheese and spoon over the chicken.
Place the dish under a very hot grill until the sauce is bubbling and is just turning golden.