Season the flour with salt and black pepper, scatter on a plate and use to coat the chicken pieces. Now heat the butter and oil in a pan ( big enough to hold the chicken and with some depth ) until foaming then add the vegetables and cook gently for 5 minutes. Remove with a slotted spoon and set aside.
Add the chicken pieces to the pan and brown on all sides (add a little more oil, if necessary).
Add the sauteed vegetables, ale, garlic, bouquet garni and season to taste. Bring to a simmer, cover and cook for 60 minutes over low heat, stirring occasionally. Half way through cooking taste broth and adjust seasonings to taste.
To serve, transfer the chicken and vegetables to a warmed serving dish. Bring the juices in the casserole to a boil then take off the heat and stir in the cream to thicken. Pour over the chicken pieces and serve.
Substitute 1 bay leaf, 1-2 tsp of dried thyme, and some fresh parsley for the bouquet garni, though best with fresh herbs.