Chris, I was surfing for recipes this morning and ran across a link on a Polish site for what Google Tranlate calls Silesian Dumplings. But for the fat in the egg yolk, there is no other fat
These may fill your requirements
potatoes cooked and whipped, cooled down
We add flour as much as 1/4 of potatoes *. We simply separate 1/4 of the potatoes and pour flour into the place. We add an egg and knead the dough. We form small balls the size of a walnut and ask a little girl to press her little finger in each dumpling. If we do not have a girl, we use for this purpose our little finger or the other end of a wooden spoon. Cook the dumplings for 5 minutes in salted water, drain them.
If we add wheat instead of potato flour, we will have ordinary potato dumplings.
* I add a little more flour - probably the potatoes in France are less flour.