Sole Meunière

Steps

1. Take the 2 soles out of the fridge 15 minutes before cooking. If the fishmonger hasn't done it, remove the dark skin: score across the skin just above the tail, lift a corner with the tip of a knife, then hold the tail in a towel and pull the skin off toward the head in one sharp tug. Keep the white skin on, scaled. Snip off the fins around the edge with kitchen shears, then pat the fish thoroughly dry with paper towels.
2. Peel the potatoes and cut them into even 1 1/2 inch (4 cm) pieces. Steam them for 20 to 25 minutes, until a knife slides in with no resistance, then keep them warm, covered, off the heat.
3. Clarify 50 g (3 1/2 tablespoons) of the butter: melt it over very low heat, skim off the white foam that rises, then gently pour the clear yellow fat into a bowl, leaving the milky whey in the bottom. Finely chop the parsley. Preheat the oven to 175°F (80°C) and put both serving plates in it.
4. Right before cooking, season the soles on both sides with salt and white pepper, then dredge them in the flour. Pat them firmly so only a thin veil remains: too much flour turns into a gummy paste instead of a crust.
5. Divide the clarified butter between two 11 inch (28 cm) skillets, or use one large oval pan, and heat over medium-high until a pinch of flour sizzles immediately. Lay each sole in flesh side down, the side you removed the dark skin from: that's the presentation side. Let it brown for 4 to 5 minutes without moving it, until the edges are golden blond.
6. Flip the sole with a wide spatula, using a second spatula to support it, and cook for 3 to 4 minutes on the other side. It's done when the flesh near the head comes away from the backbone with the tip of a knife and looks white and opaque, at 130°F (55°C) in the thickest part. Transfer the soles to the warm plates, golden side up, and return them to the oven.
7. Pour out the cooking butter and wipe one skillet clean with paper towels. Set it back over medium heat with 60 g (4 tablespoons) of fresh butter in pieces. Let it melt and foam, swirling the pan, for 2 to 3 minutes: it turns deep golden, small brown specks form on the bottom, and it smells nutty. Off the heat, immediately squeeze in the juice of half the lemon (it will foam up hard), then add half the parsley and a pinch of salt.
8. Melt the remaining 20 g (1 1/2 tablespoons) of butter over the hot potatoes, roll them in the rest of the parsley, and season lightly with salt. Pour the still-foaming brown butter over the soles, cut the other lemon half into wedges, and serve right away with the potatoes.
9. To fillet at the table, use a spoon and a fork. First push the small bones along the edges outward and set them aside. Split the flesh along the backbone from head to tail, slide the spoon under each top fillet and ease it flat toward the edge: that gives you two fillets. Lift the backbone by the tail in one motion, head and all: the two bottom fillets stay on the plate. Set the top fillets back in place and spoon the butter left on the plate over them.