In a large mixing bowl, combine the 5 cups of all-purpose flour and 1 teaspoon of coarse salt. Create a well in the center and add the whisked egg, cooking oil, and hot water. Mix until a dough begins to form. Knead the dough on a floured surface for about 5-7 minutes until it becomes smooth and elastic. Cover the dough with a towel and let it rest for at least 30 minutes.
While the dough is resting, peel and dice the russet potatoes. Boil them in a large pot of salted water until tender, about 15-20 minutes. Drain and return to the pot. Mash the potatoes until smooth, then add the farmers cheese, sautéed onions, and season with coarse salt and ground white pepper to taste. Mix well and set aside to cool.
Once the dough has rested, divide it into quarters for easier handling. Roll out one portion on a floured surface to about 1/8-inch thickness. Use a round cutter or glass to cut out circles, about 3 inches in diameter. Place a small spoonful of filling in the center of each circle.
Carefully 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 boil. Add the pierogi in batches, being careful not to overcrowd the pot. Cook for about 3-5 minutes until they float to the surface. Remove with a slotted spoon and let drain.
In a skillet, melt the stick of butter along with the 6 tablespoons of butter. Add the cooked pierogi and sauté until golden brown on both sides. Serve hot with a sprinkle of fresh herbs or additional sautéed onions if desired.