How to make white aioli?
The original Valencian allioli and Maltese aljoli don't have egg yolk in its receipe. Egg yolk makes emulsification easier but it isn't necessary. Garlic itself is already an emulsifier. 

Allioli is made by pounding garlic with olive oil and salt in a mortar until smooth. The oil should be added little by little -- otherwise the emulsion breaks.