Put the morels in a strainer and rinse well under cold running water, shaking to remove as much sand as possible. Place in a saucepan with the stock and bring to the boil over a medium-high heat. Remove the pan from the heat and leave to stand for 1 hour.
Remove the morels from the cooking liquid and strain the liquid through a fine sieve or muslin- lined strainer and reserve for the sauce. Reserve a few whole morels and slice the rest.
Melt half of the butter in a frying pan over a medium heat. Add the shallots and cook for 2 minutes until softened. Add the sliced morels and button mushrooms and cook, stirring frequently, for 2-3 minutes more. Season and add the thyme, brandy and 7 tbsp (3½ fl oz/100 ml) of the cream. Reduce the heat and simmer gently for 10-12 minutes until any liquid has evaporated, stirring occasionally. Remove the morel mixture from the pan and set aside.
Pull off the fillets from the chicken breasts (the finger- shaped pieces on the underside) and reserve for another use. Make a pocket in each chicken breast by cutting a slit along the thicker edge with a sharp knife, taking care not to cut all the way through. Using a small spoon, fill each pocket with one- quarter of the mushroom mixture and then, if necessary, close with a cocktail stick.
Melt the remaining butter with the oil in a heavy frying pan over a medium-high heat and cook the chicken breasts on one side for 6-8 minutes until golden. Transfer the chicken breasts to a plate. Add the sparkling wine to the pan and boil to reduce by half. Add the strained morel cooking liquid and boil to reduce by half again.
Add the remaining cream and cook over a medium heat for 2-3 minutes until the sauce thickens just enough to coat the back of a spoon. Adjust the seasoning. Return the chicken to the pan with any accumulated juices and the reserved whole morels, and simmer for about 5 minutes over a medium heat until the chicken breasts are hot and the juices run clear when the meat is pierced with a knife. Serve at once.