1. In a mixing bowl, combine flour and salt. Gradually add warm water, mixing until a dough forms. Knead the dough until smooth, then cover and let rest for 30 minutes.
2. While the dough is resting, prepare the filling. In a bowl, mix mashed potatoes, shredded cheddar cheese, salt, and black pepper until well combined.
3. Roll out the dough on a floured surface to about ⅛ inch thick. Cut into circles using a glass or cookie cutter.
4. Place a spoonful of filling in the center of each dough circle. Fold the dough over the filling and press the edges together to seal.
5. Bring a large pot of salted water to a boil. Add perogies in batches and cook until they float to the top, about 3-4 minutes. Remove with a slotted spoon and drain.
6. Optional: Fry boiled perogies in a pan with butter until golden brown on both sides.