Trout Amandine with Green Beans

Steps

1. Take the trout fillets out of the fridge 15 minutes before cooking. Run a finger against the grain of the flesh and pull out any pin bones you feel with tweezers. Pat the fillets dry on both sides with paper towels, then scrape the skin with the back of a knife to push out the water: dry skin crisps, wet skin sticks and tears.
2. Trim the green beans. Bring the 2 liters of water to a rolling boil with the coarse salt, add the beans, and cook uncovered for 4 to 5 minutes: they should stay bright green and still have some bite. Drain, return them to the hot pot off the heat with 10 g of the butter and a pinch of the fine salt, toss, and cover.
3. Pick the parsley leaves and chop them coarsely. Halve the lemon: squeeze one half to get 1 tablespoon of juice and cut the other into wedges.
4. Season the fillets on both sides with the rest of the fine salt and pepper the flesh side. Spread the flour on a plate, dredge each fillet, then tap it firmly to leave only a thin, even film: clumps of raw flour stay pasty.
5. In a large 11 inch (28 cm) skillet, heat the oil and 10 g of the butter over medium-high heat. When the butter foam subsides and the fat shimmers, lay the fillets in skin side down, away from you. Press on them with a spatula for 20 seconds: the skin shrinks as it hits the heat and would buckle otherwise.
6. Cook for 3 to 4 minutes without moving the fillets. From the side, you can see the flesh turn opaque from the bottom up; when only a thin translucent band remains on top and the skin is golden and releases on its own, flip the fillets and give them 30 seconds to 1 minute on the flesh side. Check: 140 to 145°F (60 to 63°C) inside, or flesh that separates into pearly flakes at the tip of a knife. Transfer to warm plates, skin side up.
7. Wipe out the skillet with a paper towel, set it back over medium heat, and add the remaining 35 g of butter with the almonds. Stir constantly: the butter melts, foams, and crackles, then the crackling quiets down. After 2 to 3 minutes, the specks on the bottom turn hazelnut brown, it smells of toasted nuts, and the almonds are golden. Take it off the heat immediately.
8. Pour the lemon juice into the butter, which bubbles hard for a few seconds, add the parsley and a pinch of salt, and swirl the pan to bring it together. Spoon the brown butter over the fillets right away, spreading the almonds evenly.
9. Arrange the green beans next to the fish with a lemon wedge and serve at once, while the butter is still foaming on the trout.