On a medium heat sear the fish in a tablespoon of olive oil for about 3 minutes each side.
Set aside on a plate and cover with a kitchen towel so the fish keeps warm but does not “sweat”.
The sauce
On a medium to low fire, melt a tablespoon of unsalted butter. Add a finely chopped shallot and cook until soft. About a minute.
Add juice of two lemons, a 1/4 cup of water, a teaspoon of sugar and on a high heat reduce to about a third of the volume. About 2 minutes.
Turn the fire to very low and blend in 3 tablespoons of cold unsalted butter, one tablespoon at a time. The trick is to keep stirring the butter and emulsify it with the lemon juice. Salt to taste.