Preparation

Make the filling

• Put the potatoes in a 4-quart saucepan with enough cold salted water to cover; bring to a boil over high heat. Lower the heat to maintain a steady simmer and cook until the potatoes are tender when pierced with a fork, about 15 minutes.
• Drain, return the potatoes to the pan, and dry them over medium heat, stirring, until they look floury and leave a light film on the bottom of the pan, about 3 minutes. Mash with a potato masher until smooth. Transfer to a large bowl and set aside.
• Heat the butter in a 12-inch skillet over medium heat. Add the onions and cook, stirring occasionally, until deep golden-brown and soft, 15 to 20 minutes. Reserve half of the onions for garnish and add the other half to the potatoes. Add the cheese, 1 tsp. salt, and 1/2 tsp. pepper and mix until well combined. Let cool to room temperature before using.

Make the dough

• Put the flour in a large bowl. Add the butter and, using your fingers, work it into the flour until the mixture has the texture of coarse meal. Add 1-3/4 cups of the warm water and stir with your fingers until the mixture begins to come together. If the mixture is dry, you can add up to 1/4 cup more warm water, 1 Tbs. at a time, until it forms a shaggy yet cohesive yet mass.
• Turn the dough out onto a well-floured work surface and gently knead it just until soft and elastic; the dough will not be completely smooth, but it should be easy to shape, with a Play-Doh-like consistency. Avoid overkneading, or the dough will become tough. (At this point you can proceed with the recipe, or let the dough rest on a floured surface, covered with a clean dishtowel, for up to 1 hour.)

Roll and cut the dough

• Line a large baking sheet with parchment and dust with flour. Divide the dough into 6 orange-size balls (about 8 oz. each). Working with 1 piece of dough at a time on a floured work surface, and keeping the others covered so they don’t dry out, roll the dough into a 1/8-inch-thick, 10- to 11-inch-wide circle.
• Using a floured 3-inch round cookie cutter or inverted glass, cut out circles of dough. Transfer the circles to the baking sheet, dust with a little flour, and top with a sheet of parchment so they don’t dry out. Repeat with the remaining dough, stacking the circles between sheets of floured parchment and rerolling the scraps until all of the dough is used.

Fill the dough

• Working with 1 dough circle at a time, brush off any excess flour and hold the circle in your palm. Spoon a scant 1 Tbs. of the filling into the center of the circle and fold it in half. Using your fingers, tightly pinch the edges together to seal and create a 1/2-inch border. Arrange the filled pierogi on a lightly floured surface or large rimmed baking sheet and dust very lightly with flour; loosely cover with plastic wrap or a clean dishtowel. Repeat with the remaining dough circles and filling.

Cook the pierogi

• Position a rack in the center of the oven and heat the oven to 175°F. Bring a 6- to 8-quart pot of salted water to a boil over high heat. Working in batches of 10 to 12, drop the pierogi into the boiling water and give them a gentle stir so they don’t stick together or to the sides of the pot. When they float to the top 5 (after 1 to 2 minutes for room temperature pierogi, 3 to 4 minutes for refrigerated, and 7 to 10 minutes for frozen), use a slotted spoon to transfer them to a platter and keep warm in the oven while cooking the remaining batches.

Serve the pierogi

• You can serve the pierogi either boiled or fried.
• For boiled pierogi, melt the butter in a 1- to 2-quart saucepan. Sprinkle the pierogi with the reserved onion and drizzle with melted butter. Serve hot with the sour cream on the side.
• For fried pierogi, melt 4 Tbs. of the butter in a 12-inch heavy-duty skillet over medium-high heat. Working in batches of 10 to 12, cook the boiled pierogi, flipping once, until goldenbrown and crusty on both sides 6 , 4 to 5 minutes per batch. Transfer to a platter and keep warm in the oven. Repeat, adding more butter to the skillet as needed. Sprinkle the fried pierogi with the reserved onion, if you like, and serve with the sour cream on the side.

Make Ahead Tips

The filling can be made up to 1 day ahead; cover and refrigerate. Filled pierogi can be covered and refrigerated for up to 2 hours before cooking, or frozen for up to 6 months; freeze in a single layer on a parchment-lined tray, then transfer to freezer bags.