I know it as Stone Porridge. These stories probably share an origin. https://sites.pitt.edu/~dash/type1548.html is sitting in my browser bookmarks, and https://en.wikipedia.org/wiki/Stone_Soup has some variations not listed on that page.
We also eat nettle soup with a boiled egg-half. I would not call it bland, it is just a dish that does not scream with its loudest voice in your face.
My dear mother told me this story when I was just a boy. I was enchanted by the idea of this magical stone, too young to consider the clever trick the tramp was playing on the woman.
The sense of cooking being a magical endeavor has stayed with me ever since.