In a small pot, add the white vinegar, 1 tablespoon of the water and pepper. Boil over medium high heat to reduce by half, about 7 minutes.
Add the remaining 1 tablespoon of cold water and allow to cool.
Add one egg yolk at a time, whisking to incorporate, until all eggs are added.
Return the bowl to medium heat and beat the egg mixture with a wire whisk to the ribbon stage (sabayon), or until the eggs triple in volume.
Remove from the heat and gradually whisk in the melted butter little by little until thoroughly combined.
Add the lemon juice, taste and adjust seasonings as needed.