In a small saucepan, melt the butter removing the milk solid fats and setting aside. You only want to be left with the yellow clear liquid.
Fill the bottom of a double boiler with 1” of water and bring to a gentle simmer.
In the top double boiler over medium heat add the egg yolks and lemon juice and whisk for 2 minutes until the color is a light pale yellow.
With your whisk moving constantly with one hand, take the other hand and slowly stream in the clarified butter. Go slow as you do not want this to congeal or cook.
Continue whisking until all the butter is incorporated.
Add in the cayenne, salt and pepper and whisk.
If the hollandaise becomes too thick, add in just a teaspoon or two of hot water.
Remove from the heat and place a lid on the pan to keep the sauce warm until ready to serve.