For the dough, in a mixing bowl, combine 3 cups of the flour and the salt and stir together with a fork. Make a well in the center and add the egg, water and oil. With the fork, gently mix together the wet ingredients, then incorporate them with the flour and salt to form a shaggy dough.
Turn out the dough on a floured work surface and knead until you form a smooth, elastic, soft dough. Add up to an additional 1 cup of flour, as needed. Wrap the dough in plastic wrap and let the rest for about 20 minutes.
Meanwhile, make the filling. In a medium skillet, heat a little neutral oil over medium heat and saute the yellow onion, stirring occasionally, until tender and golden. Season with salt and pepper. In a large bowl, mash the potatoes by hand, then add the cooked onion, cheese and salt to taste. Mix until combined.
Before you get ready to roll out and fill your pierogi, gather a strainer or colander, wooden rolling pin, 3 ½-inch cookie cutter and sheet tray. Fill a 6-quart pot with water, add a teaspoon of salt and bring to a boil.
Cut the dough in half, rewrap one half and lightly dust a work surface. Roll out the first half, making sure it does not stick to your surface, to about ¼ inch thick. Using the cookie cutter, cut out pieces close together, but not overlapping. Reserve any scraps.
In the center of each cut piece of dough, place about 1 tablespoon of the filling. Fold the dough over the filling, being mindful not to have any of the filling touch the edges. Pinch the edges together; three times is the best.
Once this batch has been assembled, repeat the process with the other half of the dough and the scraps and the remaining filling.
To cook, place about 10 to 12 pierogi at a time in the boiling water and carefully stir to ensure the heat is evenly distributed. Allow the pierogi to float to the surface. Once they begin to "dance" on the top, transfer them to a colander.
To serve, melt some butter in a large skillet, add caramelized onion and pierogi and gently toss together. Plate with dill on top and sour cream on the side.
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