Cost per Serving:
Preheat broiler. In a medium saucepan, melt 1 Tbsp. butter over medium heat. Add shallot and 1/2 tsp. salt and cook, stirring, until softened, about 3 minutes. Pour in orange juice and vinegar and bring to a boil. Cook until thick and syrupy, about 5 minutes. Remove from heat.
On a shallow baking pan, arrange fish, smooth-side down; sprinkle with remaining 1/4 tsp. salt and pepper. Broil for about 6 minutes, until fish is just cooked through. Transfer fish to a platter and keep warm.
Return reserved orange-shallot mixture to a simmer over medium heat. Gradually add remaining 7 Tbsp. butter, whisking in a little at a time until incorporated and warm, about 5 minutes. Pour the sauce over the fish and serve. Garnish with orange slices.