Step 1Spoon the capers onto paper towels, blotting the excess liquid. Heat 1 teaspoon of the olive oil in a small nonstick skillet. Add the capers and cook over medium heat, shaking the pan frequently, until capers become dry and crispy, about 5 to 6 minutes. Remove the capers from the pan and onto a plate lined with paper towels. Set aside.
Step 2Heat 3 tablespoons of oil in the same skillet over low heat until hot. Add the garlic and saute until light golden brown, 1 to 2 minutes. Stir in 2 tablespoons of the lemon juice, the oregano and salt and pepper to taste. Set the vinaigrette aside until it's time to serve the fish.
Step 3Heat 16 cups of the water in a covered fish poacher or large roasting pan along with the carrot, onion, lemon, parsley sprigs, bay leaf, salt and 4 tablespoons lemon juice. Bring to a simmer, then continue to simmer while you prepare the chard.
Step 4Remove the stems from the chard leaves and dice. Cut the chard leaves into 2-inch pieces. Heat the remaining 1 cup of the water in a medium saucepan to simmering. Add the diced chard stems; cover and cook until stems are tender-crisp, about 5 minutes. Add the cut-up leaves and continue to cook until the leaves are tender, about 5 minutes. Drain.
Step 5Toss the cooked chard with the remaining 1 tablespoon olive oil and the remaining 1 teaspoon lemon juice. Add salt and pepper to taste. Cover the chard and keep it warm while preparing the fish.
Step 6Poach the bass in the just-simmering poaching liquid until the fish tests done around the backbone close to the neck, about 10 minutes.
Step 7Lift the fish out of the pan to a large tray. Remove the head from the fish. Remove the skin from the top side of the fish and pull out any fins and visible bones.
Step 8Spoon the chard onto a serving platter. Place the fish on the bed of chard. Sprinkle the fried capers over the top of the fish and spoon the vinaigrette over, then sprinkle with the chopped tomato and parsley.