It's not really a recipe persay. I throw a clove of slightly chopped garlic in the blender (why bother mincing if you're blending), a maybe tbs size splash of apple cider vinegar or lemon juice, some salt, ummmm I don't know how much but you could add more salt after. start with maybe a 1/8 of a tsp? it's not a lot. a few grinds of pepper. and a pastured egg yolk (a regular egg yolk would work fine, but I'm iffy about eating conventional eggs raw. pastured eggs I'm totally comfortable with.)
Blend them up until smooth. Then slowly start drizzeling extra virgin olive oil into the vortex of the blender. One egg yolk supposedly absorbs a full cup of oil, however, I just add from the bottle until it gets really really thick, but a little less thick than regular mayo (my blender was a free hand-me down, and I don't think it could handle taking mayo quite to the normal thickness. a good blender should do fine). Part of the key to not breaking the mayo (having the egg and oil seperate) I've read is to add the oil really really slowly at the very begining as well as the end.
Try it with one medium sized garlic before upping it even if you like garlic, because it's raw garlic and you don't want to ruin the first batch by making it unedibly garlicy like I did my first aoili batch.
I use it like mayo(hamburgers, chicken salads, etc), but it's also awesome served as a dip for steamed broccolli. I could easily eat all of a 1 egg batch (about a cup) that way lol.