Oil and water don't mix, excpet for when they do in order to make mayonnaise. An egg yolk and an immersion blender is all you need to get an emulsification going.
I got the recipe from the Serious Eats website (http://www.seriouseats.com/recipes/2011/10/two-minute-mayonnaise.html), and was inspired to give it a try by a friend!
