Season the salmon with ¼ teaspoon of the salt. Heat a large nonstick skillet over -medium–high heat. Add the olive oil. When the oil is hot, add the salmon, and sear it on both sides, about 2 minutes per side, but don’t worry about cooking the fish all the way through at this point. Remove the salmon to a plate, pour out the oil, and wipe the skillet clean.

Return the skillet to -medium–high heat, and add 4 tablespoons of the butter. When the butter is melted, add the scallions and cornichons, and cook until wilted, about 2 minutes.

Add the Prosecco, and bring to a boil. Boil until reduced by about half, about 5 minutes. Add the remaining teaspoon salt, and slide the salmon back into the sauce. Simmer until salmon is cooked through, about 3 minutes. Whisk the remaining butter and the parsley into the sauce and serve.