Warm the milk slightly, then mix in the sugar and yeast. Let it sit for 10 minutes until foamy.
In a large bowl, sift the flour, then add the salt, egg, and melted butter.
Pour in the yeast mixture and knead the dough for 8-10 minutes until smooth and elastic.
Cover the dough with a clean kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.
While the dough is rising, prepare the filling: finely chop the onion and garlic, then sauté them in a pan with the ground meat, salt, and pepper until the meat is cooked through.
On a lightly floured surface, roll out the dough to about 5 mm (¼ inch) thick and cut out circles.
Place a spoonful of filling in the center of each circle, then fold it in half and press the edges firmly together to seal.
Heat the oil in a deep skillet to about 340°F (170°C). If you don't have a thermometer, drop a small piece of dough into the oil – if it slowly rises and turns golden brown, the oil is at the right temperature.
Fry the piroshki for 2-3 minutes per side, until golden brown. Remove them with a slotted spoon and place them on paper towels to absorb excess oil.
Serve fresh, or store in an airtight container to keep them soft.
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