I have to warn you that this mayo contains RAW EGGS. You should use it within 3 days. That said, we have eaten this in my house for about 10 years & have never become ill from it, and we use it well past the recommended 3 days. Just use eggs from a source you trust. This is delicious on homemade french fries.
a hand held blender & tall narrow container
an egg (it works best if the egg is at room temp)
a lemon or lime (I once used a clementine with tasty results)
salt, pepper, herbs & spices (garlic is good, but eat immediately, it gets stronger)
vegetable oil (I like grape seed oil, canola is also good. Olive oil makes a strong flavored mayo but it can be nice to use in combination) The amount of oil varies, depending on ... I don't really know, the egg, the lemon, atmospheric conditions. Have at least 500 ml on hand, if not more. It can take a lot.
Crack the egg into the container, squeeze in the juice of 1/2 a lemon or a whole lime & a pinch of salt & pepper, herbs & spices. Take the lid off the oil & holding the blender in the egg mix with one hand, very slowly add oil while blending. This can be tricky so you may need an assistant to provide an extra set of hands. The oil should pour in the thinnest stream possible. As the egg & oil are blended they will thicken. Keep going until you have a very creamy mayo. This takes up to 5 minutes.
Warning: for some reason the mayo does not gel when there is a thunderstorm coming.