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1
Make the crust: Finely grate parsnip (you will need 1/2 cup).
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2
Place on a clean kitchen towel (do not use paper towels), and squeeze to extract as much liquid as possible.
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3
Pulse parsnip, flour, salt, sugar, pepper, butter, cheese, and rosemary in a food processor.
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4
Add egg yolk, and pulse to combine.
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5
Drizzle ice water evenly over mixture; pulse until dough just comes together.
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6
Shape into a disk, and wrap in plastic.
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7
Refrigerate 1 hour or up to 2 days.
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8
Make the filling: Heat oil and butter in a large skillet over medium-high.
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9
Add apples and onions, and cook until golden brown, about 15 minutes.
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10
Cover, reduce heat to low, and cook until very soft and caramelized, about 35 minutes.
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11
Add vinegar and salt, and cook 5 minutes.
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12
Remove from heat and let filling cool completely.
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13
On a lightly floured surface, roll out dough 1/8 inch thick.
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14
Cut out six 7-inch rounds, gathering scraps and rerolling dough, if needed.
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15
Place on large parchment-lined baking sheets.
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16
Puree half the apple-onion mixture in a food processor until smooth.
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17
Using an offset spatula, spread 3 tablespoons apple-onion puree over each round, leaving a 1-inch border around edges.
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18
Sprinkle each with 2 tablespoons cheese.
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19
Season with pepper.
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20
Top each with a generous tablespoon of remaining apple-onion mixture, and sprinkle with 2 teaspoons cheese.
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21
Fold in edges of dough, crimping with your fingers.
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22
Refrigerate until dough is firm, about 30 minutes.
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23
Meanwhile, preheat oven to 350F.
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24
Bake until edges are golden brown, 40 to 45 minutes.
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25
Serve warm or at room temperature.
