If cooking immediately, boil a pot of water big enough to hold the batch of pierogi. Add 1 tsp salt when water begins to boil, and reduce heat to a simmer.
Have fillings ready (leftover mashed potatoes with cheese added are perfect!)
In a bowl, or on clean surface make a well in the center of the flour.
Gently add egg to well, and slowly start mixing the egg in with the flour.
Slowly add water. Use only enough to make the dough smooth and soft.
Roll dough to 1/8" thick.
Cut circles in the dough with a circular cutter about 3 1/2" in size. (Cookie cutter, glass, cup, biscuit/doughnut cutter etc.)
Re-roll dough as needed to make more circles.
Fill with about 1 tablespoon (more or less depending on your circle) of filling slightly off center.
Lightly moisten the outer edge on of half of the circle.
Fold dough over filling, and pinch edges to seal well. Ensure no air bubbles.
Sprinkle finished pieorgi with flour to avoid sticking to eatch other if layering prior to cooking.