Run the flour through a sieve onto a clean counter. Make a well and pour in a little bit of the water. Mix everything together with your hands, slowly adding more water and mixing it with the flour.
Keep going until the dough doesn’t stick to your hands, and is smooth and elastic.
Cover the dough with a clean towel for 30 minutes at room temperature. After this time, divide the dough into 2 pieces.
Dust the counter with some extra flour. Roll out one of the dough halves very thin, without breaking it.
Use an upside down glass rim to cut out circles about 3 inches in diameter. Place a tablespoon of the chosen filling in the middle of each pastry round.
Fold the edges together to make the pierogi, pressing the ends to seal it. Repeat with all the dough. It should make about 18 pierogies.
Bring a large pot of water to a boil. Add the pierogies one by one. Keep them in the pot until they float to the top after a few minutes.
After each pierogi floats to the top, let it cook for another minute in the water. Then remove it with a slotted spoon, and place them side by side in a wide plate.