In a frying pan, over medium high heat, the ground beef until cooked and evenly browned. Add onions and continue to fry until translucent. Add salt and pepper, set aside to cool.
When the dough is ready, carefully place onto a very lightly floured surface. Careful not to overwork the dough, it needs to be soft. Using your hands, roll out the dough into a long sausage shape. You want to cut into pieces that are approx the size of a golf ball. Or you can pinch off golf ball pieces from the dough. You should get at least 24 pieces from this recipe. Cover pieces you aren’t working on with cling wrap so they don’t dry out.
Shape dough balls into the shape of an oval about 4 inches across (using your hands to shape, or gently with a rolling pin). Place about 1 tablespoon of the meat mixture in the centre. Pinch both sides of the edges of the dough together, creating a seal all around. Don’t allow the filling to touch the edges or the seal will come apart. Flatten the pinches edges, or leave like a perogy.
Heat a skillet with about 1″ of oil until hot. Gently place about 4-6 piroshki into the oil (pinched side down) and cook until they’re golden brown, around 3-4 minutes. Flip over and cook other side.
Remove onto a plate lined with paper towels to absorb excess oil. Serve immediately.