Creating Pierogi with Potato and Sauerkraut is straightforward if you follow these steps carefully:

Make the Dough

1. Combine Ingredients: In a large bowl, mix the flour and salt. Create a well in the center and add the egg, warm water, and oil gradually.
2. Knead the Dough: Mix until the dough comes together. Transfer it to a floured surface and knead for about 5-10 minutes until smooth.
3. Rest: Cover with a damp cloth and allow the dough to rest for at least 30 minutes.

Prepare the Filling

4. Boil Potatoes: In a pot, bring water to a boil and add the cubed potatoes. Cook until fork-tender, then drain and mash.
5. Cook Onions: In a skillet, melt the butter over medium heat. Add the chopped onions and sauté until golden brown.
6. Combine Filling: In a mixing bowl, combine the mashed potatoes, sautéed onions, and chopped sauerkraut. Mix well and season with salt and pepper.

Assemble the Pierogi

7. Roll Out the Dough: On a floured surface, roll out the rested dough to about ¼-inch thickness.
8. Cut Circles: Use a round cutter or glass to cut out circles of dough, around 3 inches in diameter.
9. Fill the Pierogi: Place a tablespoon of filling in the center of each circle. Be careful not to overfill.
10. Seal: Fold the dough over to create a semi-circle and pinch the edges to seal tightly.

Cook the Pierogi

11. Boil: Bring a large pot of salted water to a boil. Drop in the pierogi, being careful not to overcrowd the pot.
12. Cook Until Done: Boil for about 3-4 minutes until they float to the surface. Allow them to cook for an additional minute.
13. Drain: Remove with a slotted spoon and set aside.

Optional: Sauté the Pierogi

14. Sauté: In a skillet, melt a little butter over medium heat and add drained pierogi. Cook until golden brown on both sides, about 2-3 minutes.