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1
Preheat oven to 400 degrees.
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2
Line a baking sheet with parchment paper; set aside.
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3
Bring a large pot of water to boil. Split fava pods lengthwise and slide your finger along the inside to coax the beans into a bowl. Add beans to boiling water and cook for 2-3 minutes (longer for larger beans); lift out with a slotted spoon into a strainer and rinse to cool. Pierce each fava bean's outer skin with your thumbnail and transfer inner beans to a small bowl, discarding skin. Set aside.
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4
Arrange squares of puff pastry on prepared baking dish. Bake at 400 degrees for 20 minutes.
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5
While the pastry squares bake, add fava beans, feta, chives, mint, thyme, and lemon zest and juice to the bowl of a food processor; pulse 4 or 5 times until mixture is combined and fava beans are unevenly chopped. Add salt and pepper to taste and pulse once more. (Alternately, you can mix this all together in a medium bowl, using the back of a fork to crush fava beans to your desired size.)
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6
Once the pastry squares have baked for 20 minutes, remove from the oven and spoon 1/4 of the fava mixture on top of each pastry square. Return to oven and bake 15 minutes more. Transfer tarts to a platter or individual plates. Serve sprinkled with fresh chive flowers if desired.
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7
Freeze the butter chunks for about 10 minutes before making the dough.
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8
Place flour and kosher salt into the bowl of a food processor and pulse a few times to combine. Add about 1/3 of the butter to the flour and pulse until the butter is in small crumbs. Add remaining butter and pulse 3 or 4 times, leaving visible chunks of butter. Add ice water and pulse until dough begins to clump - don't overprocess or your pastry will be tough.
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9
Turn the lumpy, uneven dough out onto a lightly floured work surface. Shape dough into a rectangle. Use a board scraper or your hands to create relatively square edges. Lightly flour a rolling pin and the top of dough rectangle. Roll back and forth to create a 12-inch by 16-inch rectangle.
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10
Fold one edge of the 12-inch side to the center of the rectangle and repeat with the opposite edge, leaving a 4-inch by 16-inch rectangle. Use your hands and dough scraper to roll dough up like a jelly roll. Roll 'jelly roll' out into a 4-inch by 16-inch rectangle. Roll it up again; wrap in plastic and refrigerate for at least 1 hour or freeze for later use.
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11
Note - After the hour has passed, I like to roll the dough out into a 4-inch by 16-inch rectangle and cut it into 6, 4-inch squares. I stack each square with a layer of parchment paper in between and freeze, then thaw in the refrigerator when I'm ready to use them. They thaw in just a couple of hours.