Season the chicken legs with salt and pepper. Heat the fat in a sauté pan, and brown the chicken on all sides, working in batches. When all the chicken is browned, remove it to a plate and add the shallots and garlic to the pan for one minute.
Pour over the Cognac to deglaze. Put the chicken back in. Pour over the wine and the stock, cover, and cook until the chicken is tender, about twenty minutes, turning once.
Meanwhile, melt a little butter in a frying pan and cook the mushrooms until golden. When the chicken is cooked, remove it to a serving platter and keep warm. Boil the cooking liquid down to sauce consistency. Stir in the cream and the mushrooms. When hot, taste and correct the seasonings. Pour over the chicken, scatter over the parsley, and serve.