Prepare the fish by rinsing and patting dry, without squeezing the delicate fish flesh. Salt and pepper both sides of the fish. Heat the oil over medium-high heat in a medium saute pan.
Cook's Note: Do not use a nonstick pan.
The oil should be glossy, but not smoking. While the oil is heating, take a fresh paper towel and pat the fish dry a second time, and dredge the fish in flour on both sides, patting off the excess. This will make your beautiful crust-searing foolproof! Place the fish in the pan and cook undisturbed for 3 minutes. Flip the fish, being firm with the spatula in order to scrape up the whole golden-seared crust when you flip. Once flipped, place 1/2 tablespoon of butter on top of each piece of fish, and allow it to melt into the saucepan. It may brown somewhat, but it should not burn. Allow the mixture to cook another 2 minutes and then remove the fish. Deglaze the pan with the lemon juice (be careful with splatters!), and quickly scrape up the brown bits of flavor. Toss in the parsley, taste for seasoning, and spoon a teaspoon of the rich lemony butter onto the fish and serve.