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1
Put flour in a large shallow bowl and make a well in center.
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2
Add water, egg, oil, and salt to well and carefully beat together with a fork without incorporating flour.
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3
Continue stirring with a wooden spoon, gradually incorporating flour, until a soft dough forms.
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4
Transfer dough to a lightly floured surface and knead, dusting with flour as needed to keep dough from sticking, until smooth and elastic, about 8 minutes (dough will be very soft).
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5
Invert a bowl over dough and let stand at room temperature 1 hour.
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6
Peel potatoes and cut into 1-inch pieces.
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7
Cook potatoes in a large saucepan of boiling salted water until tender, about 8 minutes.
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8
Drain potatoes, then transfer to a bowl along with cheese, salt, pepper, and nutmeg and mash with a potato masher or a handheld electric mixer at low speed until smooth.
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9
When mashed potatoes are cool enough to handle, spoon out a rounded teaspoon and lightly roll into a ball between palms of your hands.
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10
Transfer ball to a plate and keep covered with plastic wrap while making 47 more balls in same manner (there will be a little filling left over).
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11
Cook onion in butter in a 4- to 5-quart heavy saucepan over moderately low heat, stirring occasionally (stir more frequently toward end of cooking), until golden brown, about 30 minutes.
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12
Remove from heat and season with salt and pepper.
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13
Halve dough and roll out 1 half (keep remaining half under inverted bowl) on lightly floured surface (do not overflour surface or dough will slide instead of stretching) with a lightly floured rolling pin into a 15-inch round (1/8 inch thick), then cut out 24 rounds with lightly floured cutter.
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14
Holding 1 round in palm of your hand, put 1 potato ball in center of round and close your hand to fold round in half, enclosing filling.
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15
Pinch edges together to seal completely.
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16
(If edges don't adhere, brush them lightly with water, then seal; do not leave any gaps or pierogi may open during cooking.)
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17
Transfer pierogi to a lightly floured kitchen towel (not terry cloth) and cover with another towel.
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18
Form more pierogies in same manner.
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19
Bring a 6- to 8-quart pot of salted water to a boil.
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20
Add half of pierogies, stirring once or twice to keep them from sticking together, and cook 5 minutes from time pierogies float to surface.
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21
Transfer as cooked with a slotted spoon to onion topping and toss gently to coat.
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22
Cook remaining pierogies in same manner, transferring to onions.
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23
Reheat pierogies in onion topping over low heat, gently tossing to coat.
