Heat a frying pan until hot and add the butter and the olive oil.
Season the fish with salt and freshly ground black pepper and place into the pan when the oil and butter are sizzling hot. Cook the turbot fillets for 2-3 minutes on each side, or until golden brown all over.
For the cream foam, pour the white wine into a pan over a medium heat and bring to the boil. Boil until reduced by two thirds, then add the fish stock. Bring back to the boil and cook until the liquid has reduced by two thirds.
Add the cream, bring back to the boil and cook until the liquid has reduced by half, then season, to taste, with salt and freshly ground black pepper. Set aside and keep warm until ready to serve.
For the mushrooms, heat a clean frying pan and add the butter and the olive oil. Once hot add the shallots and garlic and fry for 2-3 minutes, until softened.
Add the mushrooms and cook for a further two minutes, then season, to taste, with salt and freshly ground black pepper and add the lemon juice and parsley.
Using a hand blender, blend the cream sauce until light and foaming.
To serve, place a large spoonful of mashed potato into the centre of each plate. Place a turbot fillet on top of each and spoon the mushroom mixture around the edge of the potato. Spoon a little of the sauce foam over the mushrooms and serve.