Shred the cabbage and sauté until done together with onion and carrot, seasoning to taste with salt, pepper, sugar and a little vinegar.
Boil the potatoes and mash with water, salt and sugar, add turmeric for color and a piece of butter. Let it cool completely.
Mix the eggs and flour into the cooled mashed potatoes and knead into a potato dough.
Shape balls about the size of a small tangerine (roughly 2 heaping tbsp of mashed potato) and place them on a floured board, coating each one well in flour.
Pour oil into a pan, as for meat patties, and set over heat.
Flatten a ball into a round patty, place the cabbage filling in the center, fold in half and pinch the edges shut like a pierogi, dusting with flour as needed.
Fry the zrazy on both sides until golden: after flipping, cover the pan with a lid. Any unfried patties can be frozen.