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  1. To make the dough: Put the flour, salt, water, and olive oil in a large bowl, and stir until the dough forms. Transfer to a lightly floured work surface and knead until the dough is smooth, elastic, soft, and doesn't stick to your fingers, about 5 minutes. Return the dough to its bowl, cover, and let it rest for 10 minutes.

  2. To make the filling: Crack the egg into a medium bowl and whisk lightly. Whisk in the feta, milk, flour, and 1 tablespoon olive oil.

  3. Preheat the oven to 375°F. Line a baking sheet with parchment paper.

  4. To assemble: Turn the dough out onto a lightly floured work surface. Divide the dough in thirds. Working with one piece at a time (keep the rest covered), use a floured pin to roll the dough into a very thin 12" square. If the dough resists as you're rolling it, let it rest a few minutes before proceeding.

  5. Brush the square with a tablespoon of olive oil. Cut the dough into four even strips, 3" wide. Place a strip vertically, with a short end facing you.

  6. Put 2 tablespoons of the filling at the top of the strip, about 1" down from the top and 1" in from the right edge.

  7. Lift the upper left-hand corner of the strip and fold it down and diagonally over the filling to meet the right edge of the dough, forming a triangle.

  8. Fold the triangle of covered filling down, much like folding a flag, to encase it in another layer of dough.

  9. Fold that triangle over on the diagonal to line up with the left side of the dough strip. Continue with these two motions until you reach the end of the strip.

  10. Place the triangle seam-side down on the prepared baking sheet. Repeat the process with the other three dough strips; then repeat with the remaining two pieces of dough.

  11. To finish and bake: Brush the triangles with the beaten egg. Bake them for 30 to 35 minutes, until they're deep golden brown. Remove them from the oven and cool for at least 15 minutes before serving. Store any leftovers in the refrigerator.