Honestly, learning to make it yourself is quite deadly. Way deadly! This stuff is nothing bug egg yolks and butter. So you might want to go for a jog both before and after you have some. I mean, it is no surprise it's French, right?
There are a couple different pan options for making this sauce. You can use a double boiler, a sauce pan, a skillet or even a stainless steel bowl. You want to use whatever you are best at controlling heat with.
Now, take your three egg yolks and the tablespoon of lemon juice and whisk it together using no heat. You want the mixture to double in size and it will have a glue like consistency and become pale.
Place the pan over a low heat and quickly add continue whisking. You want to cook the egg yolks but NOT scramble them. This is the part where most people mess up so take your time, only allowing the pan to come in contact with heat briefly. You can keep a bowl of ice water near by to dip the pan in to remove the heat if you find this step challenging. Eventually the mixture will start to really thicken, becoming almost difficult to whisk when it is done. The consistency is more like paste at this point.
By spoonfuls, add the soft butter, whisking constantly to incorporate each addition. As the emulsion forms, you may add the butter in slightly larger amounts, always whisking until fully absorbed. Continue incorporating butter until the sauce has thickened to the consistency you want. You can use more than 1/2 stick if you like.
Season the sauce with a pinch of salt and some cayenne pepper. Be careful, it is really easy to over salt this sauce.
Enjoy! I am going to have mine with this amazing Vegetarian Benedict for Eggs Benedict Day!