Once the garlic is minced, add it to the lime juice and let it sit for 20 minutes. This helps to mellow it out a bit.
Put the egg yolks, salt, lime zest, lime juice and garlic in a tall jar just wider than the blade section of the stick blender - usually a stick blender will come with its own container that can be used for this.
Blend the mixture for a minute until thoroughly mixed.
Very very slowly, drizzle in the oil while blender is going. Stop pouring when ⅓ of the oil has been added, but keep mixing and move the stick blender around, being careful not to tip over the container. The aoili will start becoming thicker after a few minutes. Keep blending and it will happen!
Start adding in the remaining oil very slowly and keep blending. You may need to move the stick up and down to fully incorporate the oil.
Refrigerate after opening. Lasts for up to 10 days.