Step 1: Prepare the Pierogi Dough

1. In a large bowl, combine the flour and salt.
2. Make a well in the center and add the egg, sour cream, and oil.
3. Gradually pour in the warm water while stirring with a wooden spoon.
4. Once the dough begins to come together, transfer to a floured surface and knead for 5-7 minutes until smooth and elastic.
5. Cover the dough with a damp cloth and let it rest for 30 minutes.

Step 2: Make the Potato and Cheese Filling

1. Place the potatoes in a large pot, cover with water, and add a pinch of salt.
2. Bring to a boil and cook until fork-tender, about 15-20 minutes.
3. While potatoes are cooking, sauté the diced onion in oil until translucent and golden.
4. Drain the potatoes thoroughly and return to the pot.
5. Mash the potatoes, then mix in the butter, sautéed onions, and cheese until well combined.
6. Season with salt and pepper to taste and allow the filling to cool completely.

Step 3: Roll and Cut the Dough

1. Divide the dough into 2-3 portions to make it easier to handle.
2. On a floured surface, roll each portion to about 1/8 inch thickness.
3. Using a 3-inch round cutter or a glass, cut out circles from the dough.
4. Collect scraps, re-roll, and cut more circles until all dough is used.

Step 4: Fill and Seal the Perogies

1. Place a tablespoon of filling in the center of each dough circle.
2. Moisten the edges of the dough with water using your finger.
3. Fold the dough over to create a half-moon shape.
4. Press edges firmly with your fingers, then use a fork to crimp and ensure a tight seal.
5. Place completed perogies on a floured surface or baking sheet, making sure they don’t touch.

Step 5: Cook the Perogies

1. Bring a large pot of salted water to a gentle boil.
2. Carefully drop 6-8 perogies into the water at a time (avoid overcrowding).
3. Once they float to the surface (about 2-3 minutes), cook for an additional 1 minute.
4. Remove with a slotted spoon and place in a colander to drain briefly.
5. Transfer to a serving dish and toss gently with butter to prevent sticking.
6. For extra flavor, sauté sliced onions in butter until caramelized and serve over perogies.