Pat the halibut cheeks dry, and season with salt and pepper.
Place the olive oil in a skillet set on medium-high heat. When very hot, add the cheeks and cook one minute on each side, or until almost cooked through. Transfer cheeks to a plate.
Drain excess oil from the skillet. Add the wine and garlic and cook until wine is reduced by half. Add the cream and bring to a simmer. Simmer and reduce the cream until it lightly thickens. Mix in the mustard and chives; season the sauce with salt and pepper to taste.
Return the cheeks to the skillet and heat them in the sauce until cooked through, about two minutes.
Divide the cheeks between two plates, top with the sauce and serve.