In the bottom half of the double boiler, bring enough water to a boil to leave space for the top half to clear the water--the boiling water should not touch the bottom of the pan, it should be heated by steam alone.
In the top half of the double boiler, off the heat and still cold, mix the egg yolks, lemon juice, mustard, water, and cayenne pepper. Stirring continuously, move the pan over the boiling water and add one of the pre-divided portions of butter.
Continuously stirring, as each portion of butter melts add another. If the sauce begins to thicken too quickly, remove it from over the boiling water and add additional butter to help cool it down. Keep stirring and adding butter until all has been incorporated.
Taste and season with salt as needed.