Begin by taking everything you need out of the refrigerator and having it ready at room temperature before you begin
Melt the butter and set aside in a pitcher or bowl. A pitcher is better if you have one because you will need to pour with one hand and whisk with the other. The butter should be very warm but not too hot to touch it with your fingers.
Take a heavy medium size tall pot and a bowl large enough to sit on top to make a double boiler. The bowl should sit over the hot water never in it. Bring about 2cm. (1inch) of water to just before boiling point. (the water should never boil).
In the bowl place the 3 egg yolks and place bowl over - not in the hot water in the pot. With a whisk, whisk the egg yolks until they become thick looking. This should take about 1 minute, (if your egg yolks were room temperature), then remove the bowl to the counter and whisk in the lemon juice and the cold water.
Turn the heat down your coming back to it soon. Remember the water should never boil. You need to know that if the egg yolks get too hot they will scramble and be good for
nothing. So take care.
Now place the bowl over the hot water again and with one hand whisk and with the other pour in the butter a small spoonful at a time, incorporating the butter into the eggs before adding the next spoonful. An electric hand held whisk turned on medium speed is really helpful to do this.
You need to keep an eye on the water in the pot and the bottom of the bowl. Lift it occasionally and touch the bottom of the bowl to see if it is getting too hot. You can keep a large bowl of cold water on the side to dip the bowl into if you think it is getting too hot and the eggs will scramble.
Keep adding the butter a bit at a time until all the butter is incorporated and remove it from the hot water. Remember the bottom of the bowl is still hot.
The sauce should be warm to the touch. Season the sauce now with salt and white pepper and you can add a spoonful or two more lemon juice if you like now. If the sauce looks too much like mayonnaise it is not a problem whisk in a spoonful at time of warm water to it to thin it out a bit.
You can hold this sauce up to an hour by keeping it in a pan of warm water.