Beaten and poached eggs
You must be referring to the New York Times article from 2006, The Way We Eat: Which Came First?

According to the author, you need a few elements in order for this to work:


Make sure you use only the "thick whites".  That means either using farm-fresh eggs, or straining away the "thin whites" with a slotted spoon after cracking the eggs.
Beat the eggs with a fork (not a whisk), and don't add salt, because the grains will tear the eggs.
Create a whirlpool in the boiling water (low boil, not rolling), which is basically to help the eggs stay suspended instead of sinking to the bottom.


According to him, the eggs take about 20 seconds to cook, after which you should strain them.

Note: Personally, I haven't tried this.  I don't know about you, but in my kitchen, it usually takes less time to make scrambled eggs in a non-stick pan than it does to boil water.  It would appear that this technique was developed due to some completely unfounded concerns about the safety of non-stick pans.  If you are still worried about safety after reading that, or just feel like experimenting, then by all means try it out.  I'm just including this little disclaimer because the NYT article gives a lot of airtime to the rumours and not much to the facts.