What is the background of brewing coffee with eggs? I hope the question isn't too broad or fuzzy. But quite a while ago, I stumbled across coffee that was prepared with eggs. The basic recipe involved mixing ground coffee with raw eggs (I think even with their shells), then cooking that mix with water and filtering it afterwards. The end result of that was in consistence and taste not much different from classic (drip, so to say) coffee, but had a notable and interesting by-taste of egg.

This was quite bit unusual to me and I didn't ever encounter this recipe again (yet am not an expert on the topic either). So I would first and foremost like to know if that preparation method is some kind of established or regional variation of coffee and how that actually developed or what the reasons/advantages for this somehow unusual combination are, be they nutritional, historical or just because it tastes good.
So I did a bit of research, and found a number of regional claims to 'egg coffee', including  Swedish, Norwegian, Vietnamese and the American Mid-West. Of course I also found an article on Putting Weird Things In Coffee, which should be taken with a pinch of salt1.
There seem to be a variety of approaches, but they seem to fall into three main camps:

Add just the white and the shell
Add just the yolk and the shell
Add the whole egg, including the shell

Across the different techniques, adding the shell was the only real unifying theme! It's said to reduce bitterness (I imagine because the shell is essentially calcium-carbonate, which is basic). The technique is to just crush up the shell, mix it and the egg contents with the coffee and pour over boiling water.
The grounds will bind with the egg protein and sink in the cup. They can then be strained off.
The only other recipe I found is specifically for Vietnamese egg coffee, which I found here:

Ingredients

1 egg
3 teaspoons of Vietnamese coffee powder
2 teaspoons of sweetened condensed milk
Boiling water

Directions
Brew a small cup of Vietnamese coffee. Crack
an egg and discard the whites. Put the yolk and the sweetened
condensed milk in a small, deep bowl and whisk vigorously until you
end up with a frothy, fluffy mixture like the one above. Add a
tablespoon of the brewed coffee and whisk it in. In a clear coffee cup
(we’re going for aesthetics here), pour in your brewed coffee, then
add the fluffy egg mixture on top. Presto. Egg coffee.


1: No, not like that.