Preheat oven to 325 degrees F (165 degrees C).
Drizzle 1 tablespoon olive oil into a large baking pan; add onion and season with salt and pepper.
Place the 2 cleaned fish into the baking pan and stuff each cavity with 1 lemon wedge, 1 rosemary sprig, and some of the red onion. Pour white wine and lemon juice over each fish and sprinkle with oregano. Drizzle the remaining 1 tablespoon olive oil over the 2 fish.
Bake in the preheated oven until fish is opaque and flakes easily with a fork, about 25 minutes. Gently slide a spatula between the bones to separate fish; remove all the bones. Serve fish on a platter and garnish with parsley and lemon wedges.
If desired, red pepper flakes sprinkled on top of fish impart a little zip to the flavor during the cooking process.
Other vegetables such as celery, pepper, or tomatoes can also be added to the pan and/or to the fish cavity.
You can also try grilling it and flipping it over once.
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