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
https://crummblle.wordpress.com/2011/10/20/kluski-slaskie-z-miesem-i-sosem/
These may fill your requirements
potatoes cooked and whipped, cooled down
potato flour
1 egg
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.