In a bowl, combine flour and salt. Beat together egg, water and oil and then stir into flour mixture making a soft but not sticky dough that holds together in a ball. If the dough is too hard, simply add water a teaspon at a time until the dough becomes soft and pliable but not sticky.
Turn out the dough onto a lightly floured surface and knead about 10 times. return to bowl cover with a damp cloth and let rest for 20 minutes.
While the dough is resting, heat butter in a skillet over medium heat, add onions, cook for 3 to 5 minutes or until golden brown. Remove from heat and transfer to a bowl. Add the mashed potatoes, cheese, salt and pepper. Stir until well mixed.
Halve the dough. With one portion of the dough at a time(leaving the other covered) roll out onto a lightly floured surface. The dough must be fairly thin, using a 3 inch round cutter or inverted glass, cut dough into rounds.
TIP Ensure that the dough is not so thin that it breaks when lifting off of the surface
Place 1 tsp potato filling in the center of each round.Lightly moisten the edge of one half of the round with water.Fold in half and pinch edges together to seal
Bring a large pot of slightly salted water to a boil. Drop perogies one at a time into the water. They are done when they float to the top. Do not boil too long or they will become soggy.
Remove with a slotted spoon and allow to drain.
Once drained they can be served or one can fry them until golden brown in a pan with onions and butter. A delicious alternative.