Garlic and oil emulsion
Congratulations, you accidentally made allioli, a Catalan emulsified sauce requiring only garlic and olive oil to thicken and emulsify.  Unfortunately, it's harder to make and less stable than the other aiolis (garlic mayonnaises), which include egg yolks as emulsifiers.  This is probably why you are having difficulty replicating it.

To make it more consistently:


Smash the garlic up into a fine paste before adding oil
Add oil slowly, starting with a drop at a time, and mixing rapidly until incorporated (traditionally this is done with a mortar and pestle, but it is easier with a mini-whisk).
Optionally, cheat and add an egg yolk (beaten) for every clove or two of garlic (it is no longer a true allioli though).