Clarify the butter by placing it in a double saucepan over simmering water until it has melted and cleared. Remove the scum from the top and carefully pour off the pure fat, leaving behind the thin milky liquid which can be discarded. Keep warm.
Put the vinegar, crushed peppercorns and shallot in a saucepan and bring to the boil. Continue boiling until reduced to a quarter of its original volume. Allow this to cool, then place it in a round-bottomed bowl over a saucepan of very hot but not quite boiling water. Add the egg yolks and water and whisk together until the mixture becomes as thick and smooth as double cream. Then very slowly add the warm butter, whisking continuously. The butter must be added slowly as it will separate if added too fast or not whisked in properly. If the mixture becomes too thick, add a few drops of warm water to thin it slightly.
When all the butter is incorporated, season with the lemon juice, cayenne pepper and salt. Pass the sauce through muslin or a fine sieve to remove both the peppercorns and the shallot. The sauce can be kept warm in a double saucepan over a low heat.