Melt butter in a saucepan; keep warm. (The butter may be kept warm by leaving the pan near a warm stove.)
Combine vinegar, pepper, and lemon juice in a saucepan. Bring to a boil and cook until reduced to half its original volume.
Add water and yolks; whisk to combine.
Cook over low heat, whisking constantly, until smooth ribbons form. Remove from heat and continue stirring to cool mixture. (If heat is too high the yolks will overcook and curdle.)
Hold pot steady using clean, dry tea towel or pot holder. Gradually, in thin steady stream, whisk warm melted butter into yolk mixture. (Once you start adding butter, do not stop until it is all incorporated. It should take 3-4 minutes to fully incorporate the butter. It is critical that the butter and yolks stay warm during this process.)
If sauce becomes too thick while adding butter, whisk in a few drops of hot water. The sauce should not appear "shiny".
Keep sauce warm.
Adjust seasoning of sauce if needed with salt, white pepper, lemon juice, and/or a tiny bit of Tabasco. Finished sauce should be light and not too thick, and evenly coat the back of a spoon.
Note: Make sure you have all your ingredients and equipment ready and together before starting.
Nutrition Facts (Per Serving): Calories 235 Cholesterol 168mg Carbohydrate 1g Protein 2g Sodium: 80mg Total Fat: 26g