In a large mixing bowl, combine the all-purpose flour and salt. Make a well in the center and add the vegetable oil, eggs, and warm water. Mix until a rough dough forms, then knead the dough on a floured surface for about 5-7 minutes until smooth. Cover with a damp cloth and let it rest for 30 minutes.
While the dough is resting, peel and dice the russet potatoes. Boil them in salted water until tender, about 15-20 minutes. Drain and mash the potatoes until smooth.
In a skillet, melt 2 tablespoons of unsalted butter over medium heat. Add the chopped sweet onion and sauté until golden brown and fragrant. In a mixing bowl, combine the mashed potatoes, cottage cheese (or sour cream), shredded cheddar cheese, and salt. Stir in the sautéed onions and mix well until combined.
After the dough has rested, divide it into two portions. Roll out one portion on a floured surface until it's about 1/8 inch thick. Use a round cutter (about 3 inches in diameter) to cut out circles of dough.
Place a heaping teaspoon of filling in the center of each dough circle. Fold the dough over the filling to create a half-moon shape. Press the edges together firmly to seal, ensuring there are no air pockets. You can crimp the edges with a fork for a decorative touch.
Bring a large pot of salted water to a gentle boil. Drop the pierogi in batches, being careful not to overcrowd the pot. Boil for about 3-4 minutes or until they float to the surface. Use a slotted spoon to remove them and transfer to a plate.
In a skillet, melt 3 tablespoons of unsalted butter over medium heat. Add the boiled pierogi and sauté until they are golden brown and slightly crispy, about 3-5 minutes on each side.
Serve the pierogi warm, garnished with additional sautéed onions or a dollop of sour cream if desired. Enjoy every delicious bite!