Beef Pierogies

1. 1In a bowl, whisk together the egg, sour cream, water, olive oil, and salt. Add the flour and stir to combine.
2. 2Dump the dough onto a floured work surface and gently knead just until the dough comes together. Do not overwork the dough. Transfer the dough to the bowl, cover with plastic wrap, and let rest for 30 minutes.

To make the filling:

1. 1In a large frying pan over medium-high heat, melt the butter. Add the onion, 1 teaspoon salt, and the sugar and cook until caramelized and brown, about 10 minutes. Add the vinegar and stir to coat. Add the carrot, thyme, and garlic and cook until tender, about 5 minutes.
2. 2Raise the heat to medium-high and add the beef. Cook, stirring to break up the meat, until it’s no longer pink, about 5 minutes. Drain the meat in a fine-mesh sieve if necessary, then transfer to a bowl. Season to taste with salt and plenty of pepper.

To assemble and cook:

1. 1Line 2 baking sheets with parchment and dust with flour. On a floured work surface, roll out the dough to 1/8-inch thick. Using a 3-inch biscuit or round cookie cutter, cut out as many rounds as possible. Press the scraps together, roll out the dough again, and repeat. You should get about 20 rounds.
2. 2Fill each pierogi with a scant 1 tablespoon of filling. Brush the edge of half the round lightly with the egg wash. Fold the round in half, pressing the edges together and crimping them to seal. Transfer to the flour-dusted baking sheet. Repeat with the remaining rounds.
3. 3Bring a large pot of salted water to a boil. Add the pierogi in batches, and cook until tender and they float to the top, 12 to 15 minutes. Using a slotted spoon, transfer to paper towels to drain.
4. 4To serve, warm half the butter and half the olive oil together in a large frying pan over medium heat. Fry the pierogi in batches until golden brown on both sides, adding more butter and olive oil as needed. Serve at once.