In a large bowl, mix the flour and salt together. Create a well in the center and gradually add the egg and water. Mix until a soft dough forms, then knead gently until smooth and elastic. Let it rest for about 20 minutes.

Peel and chop the potatoes, then boil them in salted water until fork-tender. Drain well and mash until smooth. Combine them with cottage cheese, adding a pinch of salt to enhance the flavors.

On a generously floured surface, roll the dough to about 1/8 inch thick. Use a 3-inch cookie cutter to cut out circles, ensuring you have enough for all your filling.

Place a tablespoon of the potato and cottage cheese filling on each circle. Fold the dough over the filling and pinch the edges firmly to seal them. Make sure there are no air pockets.

In a large pot, bring salted water to a gentle boil. Drop the pierogi into the water in batches, cooking until they float (about 3-5 minutes). Remove them carefully with a slotted spoon and let them drain.

In a skillet over medium heat, melt a couple of tablespoons of butter. Add the cooked pierogi and sauté until they turn golden brown and crispy on both sides, which will take about 4-5 minutes.