Natashka / Toasty soldiers

The other day, a lady saw her daughter (who was perhaps eight?) to the bus and asked the bus driver to help make sure she got off at a certain bus stop. Then she said good-bye to her daughter, calling her "Natashka".

That's not a form I had heard before; is it one of those only-for-small-children forms, presumably for Nataliya/Natal'ya? (I knew "Natasha" without the -k-.)

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Can someone tell me anything about "toasty soldiers"? I had never heard of them until I was an adult, at which point I saw them mentioned in a children's book we got from the library. From the context, it seemed like something that most British children would be familiar with.

It seems to involve strips of toast dipped in an egg, but that's as far as I've been able to gather.

Is this really something eaten commonly?

What else is involved? Is the toast toasted or "raw"? I presume the egg is soft-boiled, but with the white firm already? Does the toast usually have butter or anything else on it? How many strips do you make? Do you dip it in once and then eat the whole thing? Or bite off the eggy bit and then dip it in again until the strip is gone? Is there a typical "game" associated with eating this dish—say, dipping several strips in at once and lining them up on your plate or something? Why's it called "toasty soldiers"?

Sadly, Wikipedia seems not to have heard of it.