How to Make It
Preheat the oven to 375°. Line a large rimmed baking sheet with parchment paper. In a very large bowl, thoroughly blend the egg whites and kosher salt. On the baking sheet, form part of the salt mixture into a rectangular bed 1 inch larger than the piece of salmon and 1 inch deep. Set the salmon in the center of the salt mixture and season it inside with sea salt and pepper. Pack the remaining salt around it, pressing the salt against the fish so it adheres.
Bake the salmon for about 50 minutes, or until an instant-read thermometer inserted through the salt crust into the thickest part of the fish registers 125° if you like a rare streak, or 130° for more thoroughly cooked fish. Remove the salmon from the oven and let it rest for 15 minutes.
Meanwhile, in a small saucepan, simmer the Prosecco and scallion whites over moderately high heat until the liquid is reduced to 2 tablespoons, about 15 minutes. Reduce the heat to low and whisk in the butter, 1 chunk at a time, making sure it is fully incorporated before adding more; do not boil. Stir in the scallion greens and season with sea salt and pepper.
Using the back of a serrated knife, knock along the edge of the salt crust to crack it, then insert the knife blade to loosen the crust; carefully lift off the pieces. With 2 large forks, peel off the salmon skin and scrape off the dark flesh. Lift the fish from the bones and transfer to plates. Spoon the sauce over the salmon and serve.