Season the fish generously on both sides with salt and pepper to taste. Allow to sit for 4 minutes. Then dredge the filets in flour.
Heat a large sauce pan over high heat. Add the olive oil and gently place the filets in the pan. When the oil begins to lightly smoke, turn the heat down to medium and saute the filets on one side until they are golden brown, about 3 to 4 minutes, depending on the thickness of the filets. Turn the fish over on the other side and continue to cook until just cooked through and golden brown, another few minutes more. Remove the filets from the pan and set aside on paper towels to drain before transferring to plate.
Pour off the oil from the pan and wipe the pan with a paper towel. Return the pan to medium high heat and place the butter in the pan, melting and simmering until the butter begins to brown and takes on a nutty aromatic smell. Remove the pan from the heat and carefully add the lemon juice, zest, and capers, being careful as the liquid will react with the hot butter. Stir the mixture together and then stir in the parsley. Spoon the hot sauce over the fish. Serve immediately.