Start by making the mashed potatoes. Wash, peel and cut your potatoes into chunks and then bring them to a boil. Continue to boil for about 10 minutes or until they are fork tender. Drain the potatoes and then add in the butter, onions, salt and cheese. Mash to combine and set aside in the refrigerator to cool. Once your potatoes are cold, make your pierogi dough.
In a large bowl, mix together the eggs, sour cream, water, salt, and then slowly add in your flour. Mix to bring the dough together and then turn out onto a floured surface. If you do not have a standing mixer, use your hands to knead the dough together And if you do have a standing mixer run with the dough hook for approximately 5 to 7 minutes or until the dough is pulling away from the bowl. Once your dough has been kneaded for a few minutes, you are ready.
Lightly flour a large enough work service and using a rolling pin, roll out your pierogi dough to approximately one eighth of an inch thick. Using something with a 4 inch circle and cut out circular shapes in the dough. Spoon a small portion of mashed potatoes in the middle of the dough and after dipping your finger in a glass of water and rimming the outer circle of dough, gently fold the dough over to create a pocket. Pinch edges together until the entire pocket edge is sealed
Once your pierogi are made, simply add the pierogi to a boiling pot of water and let them boil for approximately 3-4 minutes or until they all float. You can eat them at that point as is or you can then move them to a skillet with melted butter and saute them up for two to three more minutes and then serve them immediately