If you prefer to avoid raw eggs, there's a simple alternative: If all the ingredients are blended with an immersion blender, they'll thicken and combine even without the raw egg yolk. Insert the blender into the vessel and only switch it on when it's immersed, then slowly raise and lower it. However, the mixture will only keep its consistency for a few minutes. So, it you choose the egg-free version, it's best to make the aioli right before serving.