For the Onions:

1. Melt the butter in a large skillet over medium heat. Add the oil.
2. Add the sliced onions and salt and cook, stirring frequently, for about 10 minutes or until the onions are soft and translucent.
3. Add in the brown sugar and stout and stir to combine.
4. Reduce the heat to low and cook the onions, stirring occasionally, for about 30 minutes or until deeply caramelized and soft.

For the Dough:

1. While the onions are cooking, make the dough by mixing the flour and salt together in a mixing bowl.
2. Add the yogurt, melted butter, and egg to another bowl and whisk to combine.
3. Pour the yogurt mixture into the flour and stir until a ball of dough forms. Place the dough on the counter or a cutting board and knead it for a minute or so with damp hands until the dough is smooth and elastic.
4. Place the dough back in the mixing bowl and cover with plastic wrap. Allow the dough to rest for 30 minutes.
5. For the Filling:
6. Mix together the mashed potatoes, Irish cheddar, and season, to taste, with salt and pepper.

To Assemble:

1. Bring a large pot of water to a boil.
2. After the dough has rested, roll it out on a lightly floured surface until it is ¼-inch thick. Using a three-inch biscuit cutter or glass, cut out circles of dough.
3. Place roughly 2 teaspoons of the filling in the center of each dough circle. Brush the edges with egg wash and then fold the dough over the filling, sealing the edges with your fingers. I like to press the edges together with the prongs of a fork to ensure that they are really sealed well.
4. Set formed pierogi on a sheet tray lined with parchment paper.
5. Continue until all the pierogi are formed.
6. Boil the pierogi, in batches, in the water for about 2 minutes or until they float to the top. Remove with a slotted spoon and return to the sheet tray.

To Serve:

1. Place the caramelized onions in a serving dish and wipe out the skillet.
2. Place the skillet over medium heat and add the butter. Once it is hot and starting to bubble, add in 6-8 pierogi at a time (the amount will depend on the size of your pan). Cook for about 1 minute per side or until they are crisp and golden.
3. Place the pierogi on a serving plate, drizzle over any leftover butter from the pan, and sprinkle with fresh chives. Serve immediately with the stout caramelized onions and sour cream/yogurt on the side for dipping.