Peel the potatoes and cut them into rough chunks; cut the king oyster mushrooms into pieces that are not too small. Peel the shallots and dice them finely. Heat half the butter in a saucepan and briefly fry the shallots and mushrooms, stirring frequently. Remove from the saucepan and keep warm. Heat the remaining butter, fry the potatoes, dust with flour and cook until the flour is cooked through. Pour in the cream and soup and bring to the boil, stirring constantly. Season with salt, pepper and tarragon and simmer for 10 minutes. Stir occasionally. Add the king oyster mushrooms and shallots to the potatoes and continue cooking for a further 10 minutes or so, until the potatoes and mushrooms are al dente.