Season flour with salt & pepper and dredge halibut cheeks, shaking of excess, and set aside.
Heat oil in a pan over high heat, and carefully add the cheeks. Turn the heat down to medium, and cook for 5-7 minutes until golden brown. Turn cheeks and cook for another 5 minutes.
Keeping the cheeks in the pan, pour off the oil and add the fish stock, parsley and salt & pepper. Bring to a boil, and reduce the liquid by half. Stir in the butter until melted, remove the cheeks to a warm serving platter and top with the sauce.