You can either purchase a sole skinned and trimmed for meuniere by your fishmonger or do it yourself as described in the following instructions. To trim the sole, use sharp scissors or kitchen shears to snip off the fins that surround the fillets but do not remove the tail fin. Bring a small pot of water to a rapid boil. Hold the sole by the head and dip the first inch of the tail in the boiling water for just a second or two. You should see the skin on the tail curl up and slightly peel off from the tail. Discard the boiling water. It is suggested that the next step of removing the skin be done inside a kitchen sink to help contain the sole’s small scales during the process. To remove the skin, set the sole down flat with the dark skin facing up. Use a small paring knife to gently scrape the peeled skin in the direction towards the head until it forms a “tab” which you are able to securely grab with your fingers. Use a damp dish cloth to grab this tab of skin and slowly begin to peel the skin off of the fillets going in the direction towards the head. It helps to keep the skin folded back sharply as you are pulling while simultaneously holding the tail end down with your other hand. Pull the skin off completely once at the head. Turn the sole over and repeat the process on the white skinned side. Once the skin has been removed, place the sole on a cutting board running horizontally with the thicker fillet side facing up and the larger top fillet away from you. Use a sharp knife to follow and separate the ends of the fillets where they meet the head. Begin cutting at an angle from the very top fillet down to the abdomen area. Cut all the way to the bone and then turn the fish over and repeat on that side. Use sharp shears to cut through the bones to remove the head if necessary. Discard the head. Now, beginning at the tail end, press out the contents of the abdominal cavity and discard them. Remove the tail fin and any remaining bits of side fin with scissors and discard them. Thoroughly rinse the fish and dry it well with paper towels. The sole can be stored covered in the refrigerator at this point until you are ready to cook it.
When you are ready to cook the sole, remove it from the refrigerator and pat all the fillets dry with a paper towel. Select a dish or baking tray large enough to contain the sole and add enough flour to cover the bottom by about a quarter inch. Pre-heat the All-Clad 14 inch sauté pan over medium-high heat. Season both sides of the sole generously with kosher salt. Dip each side of the sole into the flour to evenly coat the entire surface. Shake off the excess flour. Add enough clarified butter or canola oil to cover the bottom of the pan by 1/8 inch. When you begin to see the faintest wisp of white smoke emerge from the butter or oil, hold the fish by the tail end and carefully lay the thick fillet side down into the hot fat. Place the head end going in first while laying the fish down away from you to avoid potentially splashing the hot fat on yourself. Give the pan a gentle shake to make sure that the fish does not stick to the pan. Cook the fish until a dark golden brown crust is formed, approximately 4-5 minutes. You may need to adjust the heat up to promote the golden crust development or down to prevent the flour from burning. With a large slotted spatula, carefully turn the fish over and repeat on the other side. Again, adjust heat appropriately and cook for approximately another 4-5 minutes. Remove the sole from the pan with a slotted spatula and set on the desired warmed serving dish. Keep the cooked sole near the stove in order to keep it warm and to limit the distance you need to travel with the brown butter when finishing the dish. Pour the hot fat remaining in the pan out into a heat resistant container. Return the pan to the heat and turn the heat down to medium. Add the butter and swirl it around the pan until it is all melted. Cook the butter until it becomes a deep chestnut brown color. Immediately, stir in the parsley and pour the hot brown butter over the top of the sole. Sprinkle the sole with a few grains of finishing salt such as fleur de sel. Serve the sole immediately with lemon wedges. You should also serve the fish with a separate dish which can be used to set the bones on once the top fillets have been lifted off.