1Boil the potato chunks in well-salted water until completely tender, about 15 minutes. Drain well, return to the warm pot for a minute to steam off moisture, then mash until smooth. Stir in the cheddar, a good pinch of salt and plenty of pepper. Spread on a plate and let cool fully.
2While the filling cools, make the dough. Whisk the flour with 1/2 tsp salt in a large bowl. Add the egg, 1/2 cup sour cream, the melted butter and about 1/4 cup warm water. Mix and then knead on a floured counter for 5 minutes, adding a splash more water only if it feels dry, until the dough is soft and smooth. Cover and rest for 30 minutes.
3Roll the dough out to about 1/8 inch thick on a floured surface. Cut rounds with a 3-inch cutter or a glass. Put a heaping tablespoon of filling in the center of each round, fold over, and pinch the edges tightly closed so no filling peeks out. Re-roll scraps as needed.
4Bring a large pot of salted water to a gentle boil. Cook the pierogi in batches, without crowding, until they float and then 1 minute more, about 4 minutes total. Lift out with a slotted spoon onto a lightly buttered tray.
5Heat a large skillet over medium-high heat. Add the kielbasa and cook, stirring now and then, until browned at the edges, about 5 minutes. Move to a plate, leaving the rendered fat in the pan.
6Lower the heat to medium and add 1 tbsp of the frying butter and the onions with a pinch of salt. Cook, stirring often, until soft and golden brown, about 12 minutes. Scoop onto the plate with the kielbasa.
7Melt the remaining 2 tbsp butter in the same skillet over medium heat. Add the boiled pierogi in a single layer, working in batches if needed, and fry until golden and crisp on both sides, about 3 minutes per side.
8Return the kielbasa and onions to the skillet and toss everything together for 1 minute to warm through. Serve right away with dollops of sour cream and snipped chives.