In a deep bowl, combine flour and salt. Beat together egg, oil, and water. Add to flour mixture, stirring to make a soft dough.
(You may need a little more water, but don't make the dough sticky).
On a lightly floured board, knead until smooth. Divide dough in half; cover and let rest 10 minutes.
On a lightly floured board roll dough very thin, working with half at a time. Cover the remaining dough to prevent it from drying out.
Cut into 3 (8cm) inch rounds and prepare the filling.
Combine onion, butter, mashed potatoes, cheese and salt and pepper to taste and mix thoroughly.
Place a spoonful of filling on each round; fold in half to form a half circle. Pinch edges together firmly with fingers making sure they are well sealed.
Place pyrohy on a clean cloth and cover to prevent drying.
Cook pyrohy a few at a time, in a large pot of salted and boiling water for 4 to 5 minutes or until they rise to the top and are cooked through.
Drain in colander
Fry in butter until golden brown.
Serve with sour cream.