Prepare the Dough: In a large bowl, combine the flour and salt. Create a well in the center and add the egg, water, and oil. Mix until a dough forms, then knead on a floured surface for about 5-7 minutes, until smooth. Cover the dough with a damp cloth and set it aside to rest.

1. Make the Filling: Boil the potatoes in salted water until tender, about 10-12 minutes. Drain and mash the potatoes until smooth. In a small pan, melt the butter and sauté the chopped onion until golden brown. Add the sautéed onions to the mashed potatoes, then stir in the cheese. Season with salt and pepper to taste.
2. Assemble the Pierogi: Roll out the dough on a floured surface to about 1/8-inch thick. Use a round cutter or a glass to cut circles from the dough. Place a small spoonful of the filling in the center of each circle. Fold the dough over to form a half-moon shape, sealing the edges by pinching them tightly together. You can use a fork to crimp the edges for a decorative finish.
3. Cook the Pierogi: Bring a large pot of salted water to a boil. Gently drop the pierogi into the boiling water in batches, being careful not to overcrowd the pot. Boil for about 3-4 minutes, or until the pierogi float to the top. Remove with a slotted spoon and set aside.
4. Optional: For a crispy finish, heat some butter in a skillet over medium heat. Add the boiled pierogi and cook for 2-3 minutes on each side, until golden brown and crispy.