1. In a medium bowl whisk the egg. Add the sour cream and whisk until smooth. Add the milk and water and whisk until combined. Slowly add about 3 cups of flour and stir to combine with a wooden spoon.
2. Turn dough out onto a well floured surface and work in about 1 cup flour as you knead. Use a plastic scraper to lift the dough as it will stick to the counter before the flour is worked in to it. Continue kneading for about 8 to 10 minutes working in another 1/2 cup flour. The dough should be elastic in texture and no longer sticky. Be careful not to add too much flour as this will toughen the dough. Place dough in a lightly floured bowl and cover with plastic wrap and let rest while you prepare the filling.
3. Cook potatoes in salted boiling water until fork-tender. Drain and mash with a potato masher. Add melted butter and cheeses, and continue to mash until well incorporated. Season with salt and pepper to taste. Place a large pot of salted water over high heat and bring to a boil. Lay a clean linen towel on your counter and evenly distribute cornmeal on it to prevent sticking.
4. On a floured surface, roll out dough to about 1/8" thick. Using a glass or cookie cutter measuring 2 1/2" diameter cut out as many circles as possible. Gather scraps together and reroll, and continue cutting.
5. Form filling into 1 1/2" balls, and place a ball in the center of each dough circle. Holding a circle in your hand, fold dough over filling and pinch the edges forming a well-sealed crescent. Transfer to linen towel. Continue this process until all dough circles are filled.
6. Place pierogi in the boiling water in batches. They will sink to the bottom of the pot and then rise to the top. Once they rise, let them cook for about 1 more minute. Meanwhile, drizzle platter with melted butter. Remove pierogi from pot and transfer to platter to prevent sticking. Serve immediately.