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Your question is both simple and terribly complex. The complexity comes from the myriad of ways there are to make a Hollandaise and the options that you have for fats. There are arguably 5 major methods of creating a Hollandaise sauce and the fat you add is likely to be butter or clarified butter (giving 10 variations to start with), but could include any other type of fat you wanted to use. Fats that are liquid at room temperature are going to act differently than fats that are solid at room temperature. It gets to be a mess.
So instead of taking you on a grand tour of hollandaise methods, let’s talk about how the sauce works in general. A Hollandaise sauce is an emulsion sauce. You may recall a bit about emulsion sauces from The Buttercream Nemesis, which I highly recommend you read if you have not already done so. Or even if you have, really. It’s worth re-reading.
In short, what an emulsion tries to do is to get water and fat to intermingle nicely. Normally oil and fat stay as far away from each other as they can manage, but with the application of an emulsifier, such as the lecithin that is contained in an egg yolk, you can get them to spend time holding hands and creating wonderfully thick and creamy sauces.
The egg yolk is one of the problems. You see, if you heat an egg too quickly, or if you raise its temperature above a certain point, then you don’t have a beautiful emulsion, you have scrambled eggs. And not the good kind with the bacon grease (which, incidentally, you could also use in your Hollandaise). Of course, if you don’t heat the eggs enough, then any solid fats that you add won’t liquify, and you might not kill off any salmonella that could be hanging around. These are unfortunate situations both.
To kill off salmonella, you’re looking at a temperature of 160°F. Eggs curdle at 160-170°F, all things being equal. This is uncomfortably close to where you need the egg yolks, so what you want to do is to add something to the eggs to make them less likely to curdle. You can do this by adding the liquid and the fat early, and bring it all up to temperature together. Another method is to add some water or, my preference, lemon juice to the egg yolk before bringing it up to temperature. This will give you an extra 20°F to play with before the eggs curdle. As you’ll need the acid anyways, it doesn’t hurt to add it early, and will certainly help.
To make your life easier, use a room temperature fat and egg to start with, rather than a cold butter or eggs. Cold eggs will be harder to keep from curdling, and cold butter will just drop the temperature of your sauce every time you add it in.
If you break the Hollandaise sauce, it’s nearly always possible to save it. If you have the proper proportion of liquid to fat to eggs, then it’s mainly a matter of effort and some extra egg yolk. However, if you curdle your eggs, you’re doomed, and you’re just going to want to start over. Protect the eggs, and you’re safe.