Half flounders are not somehow unique to St. Louis. I found them all over the Over the Rhine neighborhood, mostly north of Liberty Street where there is more demolition and vacant lots, making it easier to see the rear of buildings. Like I had mentioned when visiting the town of Blois in France, while certainly there is a German influence throughout Midwestern architecture, I feel like the use of shed roofs is not somehow limited to one ethnic group, but is universal throughout European American architecture. See other examples below around the immediate area.

Like St. Louis, the half flounder is very common as a back service wing slanting away from the property line. There are also hipped roof flounders, as well, seen above.

There is a unique variant in Cincinnati, where the roof pitches down towards the street, seemingly without a gutter!