Combine sea salt and egg whites in a bowl and mix well. The mixture should be slightly moist.
Line a baking tray with baking paper and make a bed for the salmon with the salt mixture, about 2cm deep.
Season the inside of the salmon with salt and lay it on the bed of salt mixture. Place the remaining salt mixture over the fish and pat it down, making a sealed salt shell (it's okay if the tail pokes out).
Bake for 25-30 minutes.
Add the capers to a hot fry pan and cook for 30 seconds. Add the champagne and reduce by half. Add the butter one piece at a time and whisk until melted. Repeat with all but the last piece of butter.
Add the last piece of butter, juice of 1/2 lemon, the tarragon leaves and salt to taste. Set aside.
Remove the fish from the oven and let rest for 10 minutes.
Break open the salt crust and discard. Peel the skin from the salmon and remove the first half of the fish either whole or in portions. Remove the skeleton to access the other half of the fish.