Sift about 2 1/2 cups flour onto a bread board. Sprinkle with 1/2 teaspoon salt. Make a volcano-like crater in the flour mound and deposit 1 egg into it. Work ingredients into a dough, gradually adding about 1/2 cup cold water in a thin stream. (Some Polish cooks prefer lukewarm or even hot water.) Knead dough on floured board until firm and smooth, roll it into a ball, and let it rest 10 minutes or so beneath a warm inverted bowl. Take 1/3 of the dough at a time (leaving the rest beneath the bowl) and roll out thin. With glass or biscuit cutter, cut dough into circles. Place a spoonful of filling on each circle slightly off center, fold in half, and press edges together with fingers, crimping to ensure a tight seal. Drop small batches of pierogi into a fairly large pot of boiling salted water, making sure not to crowd them. When boiling resumes, reduce heat to a slow boil and cook about 10 minutes. Test one to see how well dough is cooked. Remove to colander with slotted spoon and rinse lightly with cold water. Serve hot with topping of choice or let them cool and fry them in butter to a nice golden brown.