Transfer the dough to a lightly floured surface and knead for about 5 minutes, until smooth and elastic. Wrap tightly in plastic wrap and let rest for 30 minutes.

While the dough rests, place the diced potatoes in a pot of salted water. Bring to a boil and cook until completely tender. Drain well, transfer to a mixing bowl, and mash until smooth.

Add the grated cheddar cheese and 1/4 cup finely chopped onion to the warm mashed potatoes. Season with salt and freshly ground black pepper to taste and mix until well combined. Allow the filling to cool enough to handle.

On a lightly floured surface, roll the rested dough to approximately 1/8 inch thick. Cut into rounds using a round cookie cutter or drinking glass.

Place a spoonful of potato and cheese filling in the centre of each dough round. Fold the dough over to form a half-moon and press the edges firmly together to seal. If necessary, lightly moisten the edge with water before sealing. Repeat with the remaining dough and filling.

Bring a large pot of generously salted water to a boil. Cook the perogies in batches, stirring gently after adding them to prevent sticking. Cook for about 5 minutes, or until they float to the surface and the dough is tender. Remove with a slotted spoon and drain.

While the perogies cook, melt the butter in a skillet over medium heat. Add the 1/2 cup finely chopped onion and sauté until soft, golden brown, and caramelized.

Serve the perogies hot, topped generously with the buttery caramelized onions and sour cream on the side.