I have been to Russian, Ukrainian and Polish restaurants and they all eat similar dumplings to the Chinese wontons. Of course they have different names of it (ie perogi, pelmeni, veriniki, etc.). I also have ate at Afghanistan, Armenian and Turkish restaurants and they also have this similar dish with different names too (manti, mantu, borek, kinkali, etc.).
I have my theory how it spread to Middle East and Eastern Europe. Chinese soldiers and merchants serving under the Mongol invasion armies must have spread it. The leader of the sack of Baghdad was a Chinese general serving under the Mongol Hulagu Khan. Merchants later followed to their court in Tabriz, Azerbaijan/Iran. In Russia, the Tatar trading quarters in Novgorod, Russia had a Chinese section.
This is a comfort food eaten when the weather is cold. This is one good thing the Mongols did in helping to spread this one part of Chinese cuisine.