Preparation / Directions:
Combine potatoes, flour, and butter, and mix briefly. Drop egg into the cold water and stir. Slowly add egg mixture to the flour mixture. Mix with spoon until it is less gooey, then knead with your hands as you would dough. Knead until the texture is smooth and even, trying to add only enough flour as needed to keep the dough from sticking to hands and table. The key is to keep a balance between water and flour so that the dough is neither too hard and heavy or too sticky. Five minutes of kneading should be plenty.
Roll out dough to 1/4" thickness. Use a glass to cut circles or simply cut the dough into small squares with a floured knife. Fill each circle with 1 teaspoon filling*, then fold over the dough and seal the edges by pinching them together firmly with floured fingertips.
Drop filled Pierogi gently into a pot of salted boiling water. Stir gently. They will sink at first - don't crowd too many into the pot. When dough is cooked (2-3 minutes), they will float. Take the finished Pierogi out and eat them or store them in the refrigerator and fry them up later.
*Fillings - Anything goes! Minced meat, fruit, vegetables... The key is to keep it dry and don't stuff too much meat in a single Pierogi or they will burst when boil