In a bowl, combine the artichoke hearts, olives, olive oil, parsley, shallots, garlic, oregano, lemon peel, salt, and pepper and toss well. Let marinate for 2 hours at room temperature.
Preheat the oven to 400 degrees F.
Lightly season the fish on both sides with salt and white pepper. Set on a parchment-lined baking sheet, skin-side up. Spoon 1/4 of the artichoke mixture on the bottom half of each fillet.
Fold the top half of the fillet over the filling. Bake until the fish is done, 12 to 15 minutes.
For the Beurre Blanc:
Combine the shallots and wine in a medium saute pan, and bring to a boil. Reduce heat to medium-low and simmer until reduced in volume by half, about 2 minutes. Whisk in the butter, 1 tablespoon at a time, adding each piece before the previous one has been completely incorporated. Continue until all the butter is incorporated and the sauce coats the back of a spoon, removing the pan from the heat periodically to prevent the sauce from getting too hot and breaking. Remove from the heat and season with the hot sauce and salt. Stir in the capers and tomatoes, and stir well. Adjust seasoning, to taste.
Remove from the oven and transfer the fish with a spatula to 4 large plates. Spoon the Tomato- Caper Beurre Blanc over the fish and serve immediately.
Yield: 4 servings