Preheat oven to 400 degrees. Skin and clean the sea bass, and cut it into 4 portions at 4 1/2 ounces each. Peel the potatoes and slice them lengthwise as thinly as you can (use a mandolin, if available).
In a pot of boiling water, blanch the potatoes for about 30 seconds: Let the slices bathe in the hot water quickly and then plunge them into a cold water bath. Place the slices on paper towels to dry.
Season the fish with salt and pepper. Next, wrap potato slices tightly around the fish, making sure they overlap. You may not need all the slices. In a non-stick ovenproof skillet, heat the oil and sear the potato-wrapped fish on all sides.
Place the skillet the oven and finish cooking the fish for about 2-4 minutes, depending on the thickness of the fish. Check the doneness by inserting a sharp paring knife in the center part of the fish. Feel the temperature "warm" on your lips.
Take the fish out of the pan and let it rest. Dump out the extra fat in the skillet and wipe it clean with a towel. In the wiped pan, add the butter, let brown, and then add the capers, chiles, tomatoes, lemon juice, parsley, salt, and pepper.
Place the fish on a plate and pour the butter sauce over it.