"I am often asked the question: What is your favorite food? Although I always answer Japanese, the real response should be and is pierogi, the delectable Polish dumplings that my mother, Big Martha, made so well in many incarnations: potato, sweet cabbage, blueberry, peach, plum, and apricot."
Make the dough: Whisk together egg and sour cream. Whisk in milk and water. Stir in flour, 1 cup at a time.
For the Dough
For the Filling
Turn out dough onto a floured surface. Using a bench scraper, turn and fold dough to knead, dusting with flour as needed, until elastic and no longer sticky, 8 to 10 minutes. (Dough will be loose and sticky. It will come together as you knead it. Be careful not to add too much flour, which will toughen dough.) Cover with an inverted bowl; let rest for 1 hour.
Holding 1 circle in your hand, fold dough over filling; pinch edges, forming a well-sealed crescent. Transfer to cornmeal-dusted towel; loosely cover with plastic. Repeat with remaining dough and filling. Working in batches, transfer pierogi to pot of boiling water. Pierogi will sink to the bottom and then rise. Once they rise, cook through, about 2 minutes more (or up to 4 minutes for plum pierogi, depending on ripeness of fruit).
For savory pierogi, coat a platter with half the butter. Transfer pierogi to platter using a slotted spoon. Drizzle pierogi with remaining butter, and season with salt. For sweet pierogi, transfer to a platter using a slotted spoon, and dot with sour cream.