Whisk egg and sour cream, add milk and water: Make the dough: Whisk together egg and sour cream. Whisk in milk and water.

Add flour gradually: Stir in flour, 1 cup at a time.

Knead dough: Turn out dough onto a floured surface. (Dough will be loose and sticky.) 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.

Rest dough: Cover with an inverted bowl; let rest for 1 hour.

Boil potatoes: While dough rests, place potatoes in a large pot, and cover with cold water. Season with salt. Bring to a boil; cook until fork-tender, 25 to 30 minutes.

Rice potatoes Drain; pass through a ricer.

Add cream cheese and butter: Stir cream cheese and butter. Season with salt and pepper.

Divide dough and prep baking sheet: Divide dough into 4 equal pieces. Line a rimmed baking sheet with a clean linen towel, and dust generously with cornmeal to prevent sticking.

Roll one piece of dough: Roll out 1 piece of dough on a lightly floured surface into a ⅛-inch-thick round (keep other pieces covered).

Cut out circles of dough: Cut out circles very close together, using a 3-inch cutter or glass. Cover with plastic wrap to prevent dough from drying. Repeat with remaining dough.

Boil water: Bring a large pot of salted water to a boil.

Fill pierogi: Place a 1 ½-inch oval (about 1 tablespoon plus 2 teaspoons) filling in center of each dough circle.

Form pierogi around filling: Holding 1 circle in your hand, fold dough over filling. Pinch edges, forming a well-sealed crescent.

Cover filled pierogi: Transfer to cornmeal-dusted towel, and loosely cover with plastic wrap. Repeat with remaining dough circles and filling.

Make brown butter: Melt butter in a small saucepan over medium heat, swirling occasionally, until dark golden brown, 8 to 10 minutes.

Cook pierogi: Working in batches, transfer pierogi to boiling water. They will sink to the bottom and then rise. Once they have risen, cook through, about 2 minutes more.

Drizzle with brown butter for serving: Coat a platter with half the brown butter. Transfer pierogi to platter using a slotted spoon. Drizzle tops with remaining butter, and season with salt.