Clarify the butter. Keep it warm but not hot.
Combine the peppercorns, salt, and vinegar in a saucepan. Reduce au sec (until dry).
Remove from the heat and add the cold water. Transfer the diluted reduction to a stainless steel bowl.
Add the egg yolks and beat well.
Hold the bowl over a hot-water bath and beat the yolks until they are thickened and creamy. Do not overcook them or they will curdle.
Remove the bowl from the heat. Using a ladle, slowly and gradually beat in the warm, clarified butter, adding it drop by drop at first. If it becomes too thick to beat before all the butter is added, beat in a little of the lemon juice.
When all the butter has been added, beat in lemon juice to taste and adjust the seasonings with salt and cayenne. If necessary, thin the sauce with a few drops of warm water.
Strain through a cheesecloth and keep warm, not hot, for service. Hold no longer than 1-1/2 hours.
To avoid having to strain the finished sauce, the diluted reduction may be strained before adding the egg yolks, but some of the flavor will be lost in the cheesecloth.
A simpler hollandaise can be made by omitting the vinegar reduction and using a little extra lemon juice for flavoring.