- Sift and measure flour with salt into a large bowl.
- Slightly beat egg with fork, and add egg to flour mixture.
- Mix in enough water to make a dough that's soft enough to roll out with a rolling pin but not so dry that it spits and cracks.
- Roll out dough on a floured bread board to about the thickness of a cracker.
- Use a large rimmed glass or a big biscuit cutter to cut rounds approximately 3–4 inches in diameter.
- Fill each round with a generous spoonful of filling, and fold dough in half to make a half-moon.
- Pinch and seal the edge of the dough with fingers then gently fold and pinch edge to make a ruffled edge with about ¼-inch folds.
- Drop each pierogi into a large pot of boiling salted water and boil until they float to the top. Remove each carefully with a slotted spoon.
- Fry the pierogi in a skillet with melted butter until golden brown.
- Serve warm or cold.