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1
Make the phyllo dough: Combine flour and salt in the work bowl of a stand mixer fitted with dough hook.
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2
Add olive oil, vinegar and 1/2 cup cold water.
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3
Mix at medium speed for about 5 minutes to obtain a smooth, soft dough.
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4
If the dough seems dry, add up to 3 tablespoons more water.
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5
Wrap in plastic film and let rest for 15 minutes.
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6
Meanwhile, make the filling: Blanch greens in salted boiling water for 30 seconds.
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7
Drain, rinse with cool water, squeeze dry and chop fine.
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8
In a small bowl, put chopped greens, parsley, dill, oregano, black pepper to taste, a pinch of crushed chile pepper and the feta.
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9
Mix with a fork to combine.
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10
Give dough a quick knead and divide into 6 pieces.
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11
Dust dough with cornstarch or rice flour, then roll each piece of dough as thinly as possible, stretching gradually to a diameter of 16 inches.
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12
Alternatively, roll dough to the thinnest possible setting of a pasta machine.
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13
Cut each circle in half and dust pieces with cornstarch or rice flour and stack off to the side.
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14
Alternatively, roll dough to the thinnest possible setting of a pasta machine and make smaller pies.
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15
Assemble the pies: Put a ridged stovetop grill or cast-iron skillet over medium-high heat.
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16
For each pie, lay 1 sheet phyllo on work surface and brush with olive oil.
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17
Cover half the sheet lightly with filling, using 3 to 4 tablespoons of mixture per pie.
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18
Fold over the other side and press down to seal pie.
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19
It will be a rough, very flat triangle shape.
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20
Brush both exterior sides with olive oil, carefully lay pie on the grill and cook for 3 to 4 minutes, until golden and crisp (reduce heat as necessary).
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21
Flip pie and cook the other side for 3 to 4 minutes, until golden and crisp.
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22
Remove and serve warm; cut into smaller pieces if desired.
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23
Continue to make pies with remaining ingredients.
