I'm watching MIT chemistry by Donald Sadoway. In one of his lectures devoted to solutions and phase separation, he performs experiments with absinthe. First he mixes absinthe with 5 $\times$ water which turns into milky louche.

Then he adds some cognac and the mixture becomes transparent again. I don't grasp his explanation of this.

Here is a timestamped link to the video.
I'll also briefly summarize his argument below:

... and why did he add cognac? ... it's cause if you have a fat phase here and you've got an aqueous phase here and if you add alcohol, you got

$(fat)\:\textrm{CH}_3 \textrm{CH}_2 \textrm{COOH} \: \dot{}\dot{}\:\textrm{OH}_2$

... this can bond to the water by hydrogen bond and this aliphatic tail can stab the fat and bring them into solution. This is why you have these recipes...

What does "stabbing the fat" mean?

Does it mean that the ethanol somehow makes the surface between fat and water disintegrate thus turning the mixture into a single phase solution? Or maybe ethanol + water + fat somehow combine to form a single molecule so that, again, there is a single phase solution now?

• To make a kind of illustration to my question: in the original mixture we have [... w w w |f f f| w w w w w |f f f f| ...] After the cognac is added to the solution we get [... wef wef wef wef ...] here w stands for water molecule, f stands for fats (whichever are there), e for ethanol and | represents a phase boundary. Is this correct? – xaxa May 5 '17 at 8:59