Adding ethanol to louche 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?
Absinthe is a strongly alcoholic beverage containing anethole, which is insoluble in water and very soluble in ethyl alcohol.  When water is added to the absinthe, the alcohol becomes too dilute to keep the anethole dissolved, and it appears milky. When more ethyl alcohol is added in the form of cognac, the solution again becomes strong enough in alcohol to dissolve the anethole and the solution becomes clear again.  

The phrase "stab the fat" is a bit odd, but I'll do my best to explain. Anethole is a fat-like or fat-loving oil, meaning it dissolves well in other fatty sorts of compounds, but not in water (which is lipohpobic, or fat-avoiding/fat-fearing). Ethyl alcohol has two parts to it. One end of it (labeled (fat) in the chemical formula in the question) is lipophilic (attracted to fat) and the other end is hydrophilic (attracted to water). If there is enough alcohol in the mixture, the lipophilic end of the alcohol molecules can surround the anethole ("stabbing the fat") which leaves the other end of the alcohol free to be dissolved in the water (and also any excess hydrophilic portions of the alcohol).  

I hope the "stab the fat" explanation was clear. Don't hesitate to ask for specific clarifications in the comments below.