Pan fry the hake in the oil over a medium heat for 2-3 minutes. Turn the fish over, add the butter and cook for a further 2-3 minutes. Season and finish by spooning the butter all over the fish.
In another pan cook the mushrooms. Add the butter and when foaming add the shallot and mushrooms. Cook for 2-3 minutes.
To make the sauce put the chicken stock into a saucepan, bring to the boil and reduce by half. Pour in the cream and reduce by half again. Finish by stirring in the wine and the butter, then season with salt and pepper.
To serve, put a hake fillet into the centre of each plate. Spoon around the sauce and top with the mushrooms.