I cook omelettes like that. I learned the technique from a friend who was a line cook at some fancy French restaurant. It works well as long as you have a very thin layer of eggs. Instead of butter, you brush a little bit of high smoke-point oil onto the pan (and mix a dash of heavy cream into the omelette batter to make up for the lost butter flavor). The eggs don't burn because they are insulated by a layer of steam.
It doesn't work for thick, American diner-style omelettes. The technique is useful because it lets you cook French-style (creamy, wet-in-the-center, made with about 100 ml of omelette batter for a 10-inch skillet) omelettes really quickly. Whereas the cooking time for a French-style omelette is typically five minutes, with this technique it is perhaps seven seconds.
Those eggs are not being levitated above the surface. I guarantee it. The pan would need be to be red hot to maintain the leidenfrost effect with a pan full of eggs. As anyone who has played around with the leidenfrost effect knows, since there is essentially no friction the little droplets of water skate around like pucks on an air hockey table. When you put your eggs in your hot pan cooking an omelette they do not float and flip out the side of the pan as they would if they were experiencing the leidenfrost effect.
The omelette does float on the pan. I see this happen every time I make the recipe.
My guess about why this happens is that, given that the omelette is a significantly large fluid droplet, the pan doesn’t actually have to be above the Leidenfrost point for the entire cooking process because it takes time for the residual steam to flow out from underneath the droplet.
