In a small saucepan, melt four tablespoons of butter. Do not let it brown.
In a medium-sized bowl, beat together four egg yolks, two tablespoons fresh lemon juice, freshly ground pepper, and salt.
To combine the eggs with the melted butter requires a little technique we like to call tempering. If you simply add the eggs directly to the warm butter, the eggs will curdle, which is not good. Unless you enjoy unattractively lumpy and congealed sauces. Which you shouldn't.
To temper the eggs, add a teaspoon of the melted butter to the egg mixture and beat with a whisk. Gradually introducing the hot liquid to the cold keeps the mixture from curdling.
Keep adding the melted butter to the egg mixture slowly until you've added about five tablespoons. Be sure to keep whisking the entire time. Really the entire time. Do not stop.
Add the egg mixture to the saucepan.
Turn the heat to low and very quickly cook the mixture — no more than 15 seconds, still whisking constantly.
If your hollandaise sauce doesn't seem thick enough, you can return to the heat and continue cooking it in five second increments — if the heat gets too high you run the risk of the eggs ending up scrambled. Keep whisking the Hollandaise sauce the entire time, until it reaches the consistency you desire.
If the sauce gets too thick, you can thin with a few drops of warm water before serving.