In a food processor, blend the flour and the salt. With the motor running, add the egg and the oil, and then pour the water in a slow, steady stream until the dough forms a ball around the blade. Transfer the dough to a floured surface and knead for about 2 minutes, until smooth. Cover with a kitchen towel and let stand for 30 minutes. Divide the dough into 2 balls. On a floured surface, with a floured rolling pin, roll out one of the balls very thinly, to about 1/16th of an inch, making sure that it doesn't tear. With a cookie cutter, or a cup, cut out circles about 3 inches in diameter. Place a heaping teaspoon of the desired filling in the middle of a circle. Fold the dough over to form a semi-circle. Brush the edges with the egg and press firmly with the tines of the fork to seal. Place the vareniki as they are made on a large, lightly floured, platter, and cover with a damp cloth, while making the next batch. Repeat with the second ball of dough. Bring 6 quarts of salted water to a boil over high heat. Reduce the heat to moderate and carefully lower half of the vareniki into the water. Boil, stirring occasionally to prevent sticking, until they rise to the surface, about 6 to 7 minutes. With a slotted spoon, carefully remove the vareniki into a colander and drain thoroughly. Transfer into a deep serving bowl and toss with half of the butter.
In a small skillet, melt the butter over medium heat and saute the onion until deeply colored, about 10 minutes. In a mixing bowl, combine the rest of the ingredients. Add the Sauteed onion along with the cooking fat and mix well. Fill the vareniki and cook as directed.
In a large skillet, saute the bacon over medium heat until it renders its fat. Remove the bacon and drain all but 2 tablespoons of fat. Add the onion and saute over medium heat until nicely browned. Turn the heat up to medium-high, add the sauerkraut and saute, stirring until limp and cooked through, about 10 minutes. Add the sugar and broth. Reduce heat to low, cover, and simmer for 10 minutes. Remove from the heat and cool to room temperature before filling. Use the reserved bacon for topping.;
Combine all the filling ingredients and mix thoroughly. Fill and cook as directed. This filling can be either sweet or savory, so add salt or sugar, accordingly. Serve with sour cream and confectioners' sugar, if sweet.
Recipe courtesy of Anya Von Bremzen, Executive Chef