Pat the fish dry with paper towels and season with salt and pepper. Pat the fillets dry a second time just to be sure to remove all the moisture. If desired, sprinkle a little flour over both sides of the fillets and use your fingers to evenly coat both sides.
Heat the oil in a large skillet (preferably cast-iron or stainless steel rather than nonstick) over medium-high heat until the oil shimmers but isn’t smoking, 1 ½ to 2 minutes.
Add the fillets to the skillet and cook, without moving, for 2 minutes. Slide a thin metal spatula underneath the fillets and carefully flip the fish.
Place a slice of butter on top of each fish fillet and cook until it springs back from light pressure, about 2 minutes. Use a spatula to transfer the fish to a platter or to 4 plates.
Carefully squeeze the lemon juice into the skillet and, with the skillet still over medium-high heat, use a wooden spoon to scrape up any browned bits stuck to the bottom of the skillet. Stir in the fresh herbs and spoon the sauce over the fish.
