Preheat the oven to 400 degrees F. Spread out sliced potatoes in a large baking pan, lightly drizzle with olive oil and season with salt and freshly ground pepper. Toss thoroughly until the potatoes are well coated. Bake in the oven, stirring occasionally, until potatoes are tender, 20 to 25 minutes.
In the meantime, combine parsley, garlic, olive oil, wine and vinegar in a food processor or blender. Process until smooth and set aside. Season to taste. Remove baking pan from oven and immediately lower heat to 350 degrees F. Pat fish fillets dry and add them to the baking pan in a single layer over the potatoes. Cover fillets with sliced onions and pour prepared sauce over the fish and onions in an even layer. Place in the oven and bake until the fish is flaky and opaque in the center, 20 to 25 minutes depending on the thickness of the fish.