In a mortar and pestle, grind up the garlic and salt to a very smooth paste, don't cheat here; it has to be very smooth.
Add egg yolks one at a time and continue to stir with the pestle incorporating well and keeping a thick, smooth consistency; add olive oil a few drops at a time and continue to stir with the pestle; keep doing this until you've used all the olive oil, your arm will be pretty tired, but I believe if you do this regularly, you will develop amazing upper body strength!
When you are finished, the aioli should be thick enough to stand the pestle upright in the aioli. If you like, add a couple of tablespoons of lemon juice for extra flavor.
Serve this over steamed potatoes, carrots, green beans, asparagus, boiled eggs, poached or pan-fried cod fish, and just about anything you want. It packs incredible flavor to just about anything, although I don't think serving it over ice cream would be a good choice here.