Corndogs are a similar concept and are common as fairground food, but with a cornbread rather than wheat bread layer.

For a traditional hot dog, though, the key thing is the toppings. Some American styles, like the Coney Island dog, can have as much topping as there is hot dog.

Pronto pups exist, which are corn dogs but made with a wheat-based batter.

Pretzel dogs and bagel dogs also exist; they sound pretty close to what OP was talking about.

https://www.google.com/search?q=bagel+dog&tbm=isch

In Denmark, this is called a "French hot dog". There isn't agreement whether it's actually inspired by something similar from France, as it appeared first 30+ years ago.

Interestingly both Germany and Poland have something similar but under different names. The German version was invented by a government food research center in an attempt to replicate Western foods: https://en.wikipedia.org/wiki/Ketwurst -- so you are right in that the top DDR food scientists also agree about the ideal hotdog shape!

For quite a while, fast food in Denmark was all about a mobile "sausage stand" (the permissions to which were interestingly given preferably to those who could not have a full time job).

In certain parts of America, we have. Klobasniky (most people just call 'em kolaches) are incredibly popular in Texas, perhaps even more popular than hot dogs.

The fun part, is that in theory, the klobasniky came from the Czech via the kolache, and then came back to Czech republic from Texas filled with meat. =)

There is a popular danish hotdog called "French hotdog" that sounds a bit like this https://danskmadpaaengelsk.wordpress.com/2014/01/29/french-h...

It's been a long time since I've been in Prague, but don't the vendors in Wenceslas Square sell normal hot-dog type buns?

http://czechoutchannel.blogspot.com/2007/05/wenceslas-square...

I remember getting American-style buns and the rolls that you're referring to. I prefer the American-style buns because when you take a bite from the roll version, the excess sauce drips out the other side, whereas you can maneuver an American-style bun such that it doesn't drip.

If it's done well, it won't drip out. See the post about Ketwurst above, that's exactly what I mean (and I didn't know it was - it seems, might be a myth - invented in GDR).

It's about the toppings! How does one do toppings in that setup? Dipping adds complexity.

How do you get the hot dog toppings (mustard, relish, onions, etc.) into the hole in the roll?

You carve out a hole slightly larger than the sausage. You hold the roll at approximately a 45 degree angle, while spinning it. Thus the hole remains in place, while the bread moves around it. As you are spinning it, you put the toppings in. Then you shove the sausage in (after acquiring enthusiastic consent).

Sauce-like toppings (mustard/ketchup/etc) are essentially put in one end before the sausage, and as the sausage is pushed in, it spreads the sauces throughout the whole sausage.

Some others (fried onions, etc) get put in with a long spoon before the sausage.

see Hawaiian "Puka Dog"s.

That is a quiche