The thought of making your own mayonnaise or hollandaise may seem daunting to even the most dedicated home cook. However both of these sauces, as well as hundreds of others, fall under the same principle of emulsification, which I promise is not as scary as it sounds.
Emulsifying a sauce essentially means to combine two liquids that would normally not mix, with the help of an "emulsifier." For example, think of your standard salad dressing: oil and vinegar. When placed into a container together, the oil sits atop the vinegar, refusing to mix for longer than a few fleeting moments after a good shake. But, when an emulsifier is whisked into the party, such as an egg yolk or some Dijon mustard, the dressing becomes thicker and more cohesive. Voila: an emulsion.
In culinary school, we break this concept down even further into warm emulsions and cold emulsions. A cold emulsion, like a mayonnaise, requires only agitation with a whisk to emulsify and thicken, whereas a warm emulsion, such as a hollandaise, needs some heat. I'm not going to lie; warm emulsions are extremely fussy and can easily "break." But don't fret if you have a few disastrous hollandaise; practice makes perfect...and perfect eggs benedict.
Begin by heating up water in a double boiler. You could also fill a small pot with a little water and place a non-reactive bowl inside of the pot, ensuring that the bottom of the bowl does not touch the water. You want the water to be at a light simmer the whole time, not a boil.
Whisk the egg yolks and water or cream together for about 4 minutes, or until the mixture is thick, frothy, and you can see the bottom of the bowl while whisking. Next, add the warm clarified butter in a slow, steady stream, whisking constantly. Take the bowl on and off the heat to ensure it does not get too hot, or it will break apart. You also cannot let it get too cold, as it could also break.
When the sauce is as thick as you desire (thinner than a mayonnaise but thicker than a cream sauce), stop adding the butter. Add a squeeze of lemon, salt, and cayenne to taste, and serve immediately to minimize the risk of curdling.