In a medium saucepan, completely melt the butter over medium-low heat. Remove the pan from the heat and set it aside for 5 minutes. Skim and discard the white foam that rises to the surface of the butter. Carefully ladle or pour the clear golden butter into a container with a pouring spout. Take care not to add the milky solids and watery liquid at the bottom of the pan. Set the butter aside in a warm spot.

Fill a medium saucepan with a couple inches of water, and bring to a simmer over medium heat.

In a medium heatproof bowl, combine the egg yolks and the cold water. Whisk until the yolks are light and frothy. Place the bowl over the simmering water and whisk constantly and vigorously until the yolks are thickened and light, about 3 to 4 minutes. (If the eggs begin to scramble or the mixture is cooking very quickly or gets too hot, remove the bowl from the heat and whisk to cool). Remove the eggs from the heat and whisk for 30 seconds to cool slightly.

Remove the saucepan from the heat and set the bowl over the hot water. Slowly drizzle the butter into the eggs while whisking constantly. Whisk in the lemon juice, salt, and pepper to taste. (If the sauce is very thick add a few drops of warm water to adjust the consistency so it is creamy and light.) Serve immediately or keep the hollandaise sauce in a small bowl set over warm, but not hot water, for about 30 minutes or in a warmed thermos for about an hour.