Greeks separate egg yolks and froth egg whites and then temper in some hot broth to the egg yolks. Then they mix warm yolks with white froth. Then add to soup which will thicken it and also give a good flavour, usually done with lemon. It's called avgolemono
The technique shown in the video falls, more or less, under the general technique called Braising:
a combination-cooking method that uses both wet and dry heats: typically, the food is first sautéed or seared at a high temperature, then finished in a covered pot at a lower temperature while sitting in some (variable) amount of liquid (which may also add ...
This would generally be known as a variant of "basted eggs".
The idea of basted eggs is to apply heat from the bottom (from the pan) without flipping, but additionally cook the tops with liquid. The two ways of doing this are (1) to spoon hot fat over the eggs, or (2) to add water and cover the pan to allow steam to cook the tops.
My normal method ...
I want to do the same thing.
Here's an article about acidification and its effect on pathogens in commercial egg pickling.
It basically says that eggs must be held in refrigeration while approaching the correct acidity of less than or equal to 4.6 pH, but that the bacteria won't actually die until the acidified eggs ...