In a large bowl, mix flour and salt. Gradually add warm water, mixing until a dough forms. Knead the dough on a floured surface until smooth. Cover and let rest for 30 minutes.
In another bowl, combine mashed potatoes, cheddar cheese, salt, and pepper. Mix well.
Roll out the dough on a floured surface to about ⅛ inch thickness. Cut into circles using a glass or cookie cutter.
Place a spoonful of filling onto each dough circle. Fold the dough over the filling and press the edges to seal.
Bring a large pot of salted water to a boil. Cook perogies in batches until they float to the top, about 3-5 minutes. Remove with a slotted spoon.
Optional: Fry boiled perogies in a skillet with butter until golden brown on both sides.