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1
Prepare the dough: combine the flour, yeast, salt, water and butter in the bowl of a stand mixer fitted with a dough hook and knead for about 10 minutes to a soft and slightly sticky dough.
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2
Lightly flour the dough in the bowl, cover with plastic wrap and let rise for about 30 minutes, until doubled in volume.
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3
Punch the dough down and divide it into 6 equal-sized balls.
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4
Cover with a kitchen towel and let rise for another 15 minutes.
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5
Preheat the oven to 400F.
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6
Line two baking sheets with parchment.
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7
Prepare the filling: combine the cottage cheese, egg, mozzarella and feta in a bowl.
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8
With a rolling pin, stretch and flatten the dough into an oval sheet 1/3-inch thick.
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9
Divide it into 6 equal portions.
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10
Work with one piece of dough at a time: Place one-sixth of the filling in the center of an oval.
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11
Spread to within 1 inch of the edges.
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12
Roll the edges over to make a thick rim, pinching the narrow sides of the oval together to form a point at the ends.
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13
The pie should look like a kayak (see the photograph).
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14
Fill and shape the rest of the pies in the same manner.
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15
Slide the pies onto the baking sheets and place on the bottom rack of the oven.
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16
Bake for 12 to 15 minutes, until the crust is golden and the bottom is firm and crusty.
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17
Remove the pies from the oven, leaving the oven on.
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18
Prepare the topping: break the eggs, one at a time, into a small bowl and carefully slide each into the pie.
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19
When all the pies are filled with the eggs, return the pan to the oven and bake for 5 minutes.
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20
Top each pie with a small cube of butter and serve immediately.
