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To make the dough: In a large mixing bowl, mix and knead all of the dough ingredients until smooth. Cover the mixing bowl and let the dough rise for 1 hour.
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Divide the dough into 14 pieces (2 1/2 ounces each) and shape each into a firm round. Cover and refrigerate overnight.
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To make the filling: Add the salt to the spinach leaves and rub together thoroughly. Drain in a colander for 1 hour. Rinse well under cold water, then squeeze out as much liquid as you can. Chop the leaves coarsely, then mix with the remaining filling ingredients.
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To shape and assemble: Place a rack in the upper third of the oven and place a pizza stone on it, if you have one; if you don't have a stone, no worries. Preheat the oven to 500°F before you begin to assemble the breads – the stone needs at least an hour to be fully heated and ready to bake.
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Roll each ball of dough on a lightly floured surface into a 5"-diameter circle. Place 1/4 cup of filling in the center of each flatbread, leaving a 1/2" rim of dough clear all around. Lightly brush or spritz water onto the rim. Take a third of the circle and pull it up and over the filling. Take the next third of the circle and bring it up to meet the first, then fold up the remaining third of the dough to enclose the filling. You will have made a triangle-shaped packet.
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Pinch all of the seams together, then place, seam side down, on a parchment-lined baking sheet. Brush each piece lightly with olive oil.
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To bake: Place the baking sheet onto the stone, or onto the oven rack. Bake the flatbreads for about 8 minutes, until they're medium brown; the bread should still be soft after baking. Remove from the oven and serve warm.
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Storage information: Store any leftovers in the refrigerator, well wrapped, for several days.