Sprinkle the chicken with salt and pepper. Heat the fat in a saute 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 1 minute. Pour in the Cognac to deglaze. Put the chicken back in the pan. Pour in the wine and stock, cover and cook until the chicken is tender, about 20 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 creme fraiche and mushrooms. When hot, taste and correct the seasonings. Pour the sauce over the chicken, sprinkle with the parsley and serve.