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1
In a bowl, whisk together the egg, sour cream, water, olive oil, and salt.
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2
Add the flour and stir to combine.
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3
Dump the dough onto a floured work surface and gently knead just until the dough comes together.
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4
Do not overwork the dough.
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5
Transfer the dough to the bowl, cover with plastic wrap, and let rest for 30 minutes.
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6
In a large frying pan over medium-high heat, melt the butter.
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7
Add the onion, 1 teaspoon salt, and the sugar and cook until caramelized and brown, about 10 minutes.
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8
Add the vinegar and stir to coat.
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9
Add the carrot, thyme, and garlic and cook until tender, about 5 minutes.
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10
Raise the heat to medium-high and add the beef.
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11
Cook, stirring to break up the meat, until its no longer pink, about 5 minutes.
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12
Drain the meat in a fine-mesh sieve if necessary, then transfer to a bowl.
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13
Season to taste with salt and plenty of pepper.
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14
Line 2 baking sheets with parchment and dust with flour.
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15
On a floured work surface, roll out the dough to 1/8-inch thick.
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16
Using a 3-inch biscuit or round cookie cutter, cut out as many rounds as possible.
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17
Press the scraps together, roll out the dough again, and repeat.
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18
You should get about 20 rounds.
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19
Fill each pierogi with a scant 1 tablespoon of filling.
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20
Brush the edge of half the round lightly with the egg wash.
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21
Fold the round in half, pressing the edges together and crimping them to seal.
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22
Transfer to the flour-dusted baking sheet.
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23
Repeat with the remaining rounds.
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24
Bring a large pot of salted water to a boil.
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25
Add the pierogi in batches, and cook until tender and they float to the top, 12 to 15 minutes.
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26
Using a slotted spoon, transfer to paper towels to drain.
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27
To serve, warm half the butter and half the olive oil together in a large frying pan over medium heat.
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28
Fry the pierogi in batches until golden brown on both sides, adding more butter and olive oil as needed.
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29
Serve at once.
