Place juices and ginger in a small saucepan over medium-high heat; cook until reduced by half, ~6 minutes; remove from heat; set aside.
Place butter and olive oil in a large skillet over high heat; season halibut with salt and pepper; when butter is melted and hot, place the fish skin side up in the skillet to sear ~3 minutes.
Line a baking sheet or broiler pan with foil; brush foil with some of the butter in the skillet.
Place halibut, seared-side-up, on the foil; brush top of fish with the remaining butter from the skillet; sprinkle with lemon zest.
Bake ~12 minutes, until fish flakes easily with a fork.
Nutrition Facts: Servings: 8; Amount per serving: Calories 555; Total fat 36.5g 56%; Saturated fat 8.6g 43%; Cholesterol 121mg 40%; Sodium 1208mg 50%; Carbohydrates 13.2g 4%; Fiber 4.1g 29%; Sugars 0.5g 1%; Protein 47g 94%; Based on DV of 2000 calories per day
Why does this matter? A bit of olive oil with melted butter will prevent the butter from scorching (browning/burning)