2 egg yolks (or egg whites for lighter flavor)
1 t mustard (optional)
1/4 t Cayenne pepper
2 T vinegar (brown or white vinegar. or lemon juice)
1 c oil (vegetable or olive or a combination)
salt and pepper to taste
pinch of onion powder (optional)
Put 1 cup of oil into a container that you can use to drop it into the mix but drops. I use a large eye dropper and a cup.
Add egg yolks (or whites) to a bowl and whisk in everything but the oil. When ready begin dropping in the oil, just a few drops at a time while continuing to whisk. It's hard work but the end result is worth it. Keep at it, just a few drops at a time, otherwise it will not thicken. When you used about 1/2 to 3/4 of your oil you can then start to drizzle it in slowly.
It might work better and easier with a food processor but I do things by hand and don't own one.
I sometimes make it with yolks, sometimes with white and have tried using 1 whole egg. I prefer the yolks my son prefers the whites. The lemon juice version is ok but not mayo like at all to me. We both prefer the vinegar.
It stays good maybe up to a week but because it has raw egg it should be used in a few days. I would never make this with commercial eggs but because we raise our own and know how fresh and healthy they are I have no problem with it. We even get to lick the bowl when I make cakes.