In a mixing bowl, combine the water, oil and egg. Mix well. Add the salt and 3 cups of the flour. Mix until the dough comes together and form a smooth ball (see Cook's Note). Cover with plastic wrap and allow to rest for 30 minutes. For the filling: Pass the potatoes through a hand ricer. In a bowl combine the potatoes, cheese and oil. Mix well. Season with salt and pepper. Set aside. Turn the dough out onto a floured surface and roll to a square, about 14 inches and 1/4-inch thick. Cut the dough into3 inch squares. Place a spoonful of the filling in the center of each square. Wet the edges of the dough with a little water and fold the dough over to form triangle. Seal the edges completely. Bring a pot of salt water to a boil. Add the triangles and cook for about 4 to 5 minutes or until the triangles float for 1 minute. Remove and drain on paper towels. In a large skillet, melt half of the butter. Pan-fry the dumplings in batches. Cook until golden both sides, about 2 minutes. Remove and drain on paper towels. Season with salt. Serve warm with the sour cream and pickled red onions.
If the dough is too sticky-add a little more flour, about 1/4 cup at a time.