In a medium bowl (blender, food processor), mix the yolks, mustard, if using, and 1 teaspoon lemon juice.
2 egg yolks, 1 teaspoon mustard, 3 teaspoon lemon juice
Start whisking vigorously (blender or food processor on low) while dripping the oil very slowly, even drop by drop in the beginning. You’re creating an emulsion, and if you put too much oil at once, it will separate and will be very hard to save. Whisk non-stop and use a towel under the bowl to help stabilize it.
½ cup olive oil, ½ cup coconut oil, 1 cup liquid bacon fat or rendered lard in place of the olive and coconut oils
As you add more oil, the emulsion will form, and the mayonnaise will start to thicken you can pour the oil faster at this point.
When all the oil is incorporated, and the mayonnaise is thick, whisk in the rest of the lemon juice and taste your creation. You can season to taste with salt and pepper.
Enjoy without guilt, and keep the leftovers in the refrigerator!