Potato pierogi get a lighter, brighter flavor with the addition of green peas in the filling; the dough recipe is Martha's mother's.
In a medium bowl, whisk together egg and sour cream. Whisk in milk and 1/2 cup water. Gradually stir in flour until a loose, sticky dough forms.
Turn dough out onto a floured surface. Using a floured bench scraper, turn and fold dough to knead, dusting with more flour as needed, until elastic and no longer sticky, 8 to 10 minutes. (Don't add too much flour; it will toughen dough.) Cover with an inverted bowl; let rest 1 hour.
Cover potatoes with cold salted water in a large pot. Bring to a boil over medium-high; cook until fork-tender, 25 to 30 minutes. Drain; pass through a ricer. Stir in cream cheese and melted butter. Add 1 1/4 teaspoons salt and 1/4 teaspoon pepper.
Prepare an ice bath. Bring a small pot of salted water to a boil over medium-high. Add peas and cook until tender, 3 to 6 minutes. Transfer to ice bath. Drain; transfer to a food processor and puree. Stir into potato mixture.
Divide dough in half. Line two rimmed baking sheets with towels; dust with cornmeal to prevent sticking. On a lightly floured surface, roll out one piece of dough 1/16 inch thick. Cut out 3-inch circles. Cover with plastic wrap. Repeat with remaining dough. Meanwhile, bring a large pot of salted water to a boil.
Place 1 tablespoon filling in center of each circle. Holding one circle in your hand, fold dough over filling to form a crescent. Pinch edges to seal. Transfer to a cornmeal-dusted towel; loosely cover with plastic wrap. Repeat with remaining circles and filling.
Melt remaining 1 1/2 sticks butter in a saucepan over medium, swirling occasionally, until dark golden brown, 8 to 10 minutes.
Working in two batches, transfer pierogi to boiling water. Once they rise to the top, cook through, 2 minutes more. Coat a platter with half of brown butter and transfer pierogi to platter. Repeat with remaining pierogi. Drizzle with remaining brown butter. Season with salt; serve.