Melt the remaining 4 tablespoons of butter in the saucepan. Add the onion and shallots and cook over moderate heat until softened. Add the wild mushrooms and cook, stirring occasionally, until tender, about 20 minutes. Add the Cognac and cook until evaporated. Stir in the stock, thyme sprigs, bay leaves and cooked white mushrooms and bring to a simmer. Reduce the heat to moderately low and cook for 45 minutes. Discard the thyme sprigs and bay leaves.