No review websites seem to contain this venue but it's TA #1 which probably explains why there's a good deal of Americans there. Having said that now that I've been I can see why they visit.
Walking in you get hit in the face with a steamy humid atmosphere likely from the hot soup, the wait staff moving around, the human bodies and piled high insulated jackets. The menu is simple - shellfish soup or lamb soup in a bowl (1390ISK) or in bread (1890ISK), or the fisherman's fav 2000ISK which comes with sweet rye bread.
Both soups are excellent and full of flavour. The lamb had a deep earthy salty flavour and the meat itself was remarkably tender. The shellfish soup was creamy and contained little prawns and scallop pieces. It comes with unlimited refills which the staff are more than happy to provide (although there may be a short wait if busy or they are creating more soup). If the bread bowl has been eaten or disintegrated beyond repair they give refills in a bowl instead.
The fisherman's fav is a mash of cod and potatoes and tastes as such. It's fine but the soups are much better. I'm not sure if it comes with refills but I didn't like it enough to get more. I did see another table ask for more bread and given sliced loaf instead of the rye.
Probably the cheapest all-you-can-eat in Iceland.