Pat the Dover Sole dry with paper towels and season both sides with Salt and Black Pepper.
Lightly dredge the fish in Plain Flour, shaking off any excess so the coating is thin and even.
Heat a large skillet over medium-high heat and add a splash of Neutral Oil plus a generous knob of Butter; when the butter has melted and the pan is hot but not smoking, lay the sole in the pan.
Cook the sole undisturbed until the underside is golden-brown (about 2–3 minutes depending on thickness), then carefully flip and cook the other side until just cooked through — the flesh should flake easily and remain moist.
Transfer the cooked fish to a warmed plate and tent loosely with foil to keep warm while you make the sauce.
Reduce the heat to medium-low, add a little more butter to the skillet and let it melt and brown slightly until it smells nutty; stir in Lemon Juice and scrape up any browned bits from the pan to make a glossy sauce.
Spoon the lemon-butter sauce over the fish, scatter chopped Flat-Leaf Parsley on top, and serve immediately.
