The person who devised it was Kanno Katsue, one of the very many people repatriated from Manchuria at the end of the war. She took the boiled dumplings she had known over there as a starting point, and arranged them in a circle in an iron pan, so that a large number of them could be cooked all at once.
In 1953 she opened a shop in Fukushima city called Manpuku, which means a full stomach. That is not a coincidence, and it was certainly not marketing. In a period when eating at all was difficult, her stated intention was to fill people up.
White rice was scarce and expensive at the time. A single plate of dumplings that could actually put an end to hunger was a serious proposition, and word spread through the town on exactly that basis.
When the dumplings are done, the pan is inverted straight onto a plate, so what arrives at the table is a complete circle, crust facing upward, with everyone reaching into it from their own side. Many of them at once, shared out between however many people happen to be sitting there. The name of the shop states the objective plainly, and the shape of the thing is simply the most efficient way of achieving it.
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