Chop the onion into small pieces and fry in olive oil.
Chop the sauerkraut and squeeze out excess juice. In a pot, boil water and put the sauerkraut in. Grate the carrot and add to the pot.
Cook for about 30 minutes until the cabbage becomes soft. Drain it well.
Add the sauerkraut/carrot mix to the fried onion, combine and fry together for 10-15 minutes. Season with the right amount of salt and pepper. Set aside.
Choose one of the dough recipes from here, or follow this basic recipe below.
Sift the flour onto your work surface. Make a well, pour in a small amount of hot water.
Knead quickly, gradually adding enough water for the dough to become soft and elastic. Don't add too much, because it might become too sticky.
Divide the dough into four parts. Spread the first on a work surface sprinkled with flour. Roll into a thin piece of dough. Cut into circles using a round cutter (or a glass).
Place a spoonful of sauerkraut filling in the middle of each circle. Fold dough over filling. Press edges together.
Continue until you're out of ingredients.
Bring a pot of salted water to a boil, then reduce the heat.
Drop in a couple of dumplings. Cook for 5 to 6 minutes - until they start to float to the top.
Collect pierogi with a slotted spoon. Serve with melted butter or other topping of choice.