Add the egg yolks and whole egg to a food processor and turn the machine on, pureeing for approximately one minute.
Turn the machine off and add the lemon juice plus a pinch of salt and pepper. Add the garlic, if using. Puree for another 30-60 seconds.
With the machine running, slowly add the olive oil until completely emulsified. The sauce should be thick and pale in color. If the funnel-shaped food pusher that comes with your food processor has a small hole in the bottom, the olive oil can be poured through the top. That will allow the oil to be added at the perfect speed.
Once the oil has been added, taste and add more salt and pepper to taste if desired. This is also a good time to add additional flavors such as cayenne pepper, Sriracha, pesto, etc.
This will keep in the refrigerator for up to 2 weeks, but is best enjoyed within 1 week.
I find that using extra virgin olive oil results in a bitter aftertaste. If you can't find regular olive oil (or don't want to buy it), you can use a neutral-flavored oil, such as canola or grapeseed.Since the eggs are consumed raw, it's safest to use pasteurized eggs, which have been heated to a temperature that kills many of the harmful bacteria.