Directions

1. Make the dough: In a medium bowl, whisk egg. Add sour cream, and whisk until smooth. Add milk and water, and whisk until combined. Slowly add about 3 cups flour, and stir with a wooden spoon to combine.
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 dough as it will stick to the counter before flour is worked in. Continue kneading for 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 dough. Place dough in a lightly floured bowl and cover with plastic wrap; let rest while you prepare filling.
3. Make the filling: Place potatoes in a large pot, and cover with cold water. Add salt. Place over high heat, and bring to a boil. Cook until fork-tender. Drain and mash with a potato masher. Add 8 tablespoons melted butter and the cheeses, and continue to mash until well incorporated. Season with salt and pepper to taste.
4. On a floured surface, roll out dough to about 1/8-inch thick. Using a glass or a cookie cutter measuring 2 1/2 inches in diameter, cut out as many circles as possible. Gather dough scraps together, roll them out again, and continue cutting.
5. Lay a dry, clean towel on work surface; set aside. Place about 1 1/2 tablespoons of filling 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 towel. Continue this process until all dough circles are filled.
6. Bring a large pot of water to a boil over high heat. Place pierogi in 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 a minute more. Meanwhile, In a small saucepan, cook remaining butter over medium-high heat until nut-brown in color, about 6 minutes. Remove pan from heat and drizzle butter onto a serving platter, leaving any burned sediment behind. Remove pierogi from pot, and transfer to platter to prevent sticking. Serve immediately.