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PASTRY:.
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In a food processor, pulse the flour, sugar and salt.
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Add butter and pulse until it's the size of small peas.
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Add the ice water and pulse until dough forms.
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Turn out onto a work surface and gather the crumbs together.
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Shape into a disk.
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wrap in plastic and refrigerate for an hour.
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FILLING AND STREUSEL:.
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Mix flour with walnuts, both sugars, 1/4 teaspoon salt and cinnamon in a medium bowl.
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In a small skillet, cook five tablespoons butter until golden brown.
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Pour over flour mixture and toss gently until crumbly.
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Refrigerate.
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Preheat oven to 375F.
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In a large skillet, bring the maple syrup, vanilla bean and seeds to a boil.
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Cook over moderately high heat for three minutes.
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Whisk in the remaining butter and 1/4 teaspoon salt.
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Add half of the apples and cook until beginning to soften.
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Transfer apples (with slotted spoon) to a platter.
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Repeat with remaining apples.
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Let cool.
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Discard the vanilla bean and scrape pan juices into a bowl.
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On a lightly floured work surface, roll out the pastry to a 15-inch round, 1/8 inch thick.
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Transfer to a baking sheet and refrigerate 15 minutes.
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Brush the egg wash in a 2-inch band around the edge of the dough.
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Spread apples on the pastry.
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Add any pan juices.
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Fold the border up over the apples, leaving the center exposed.
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Sprinkle the streusel topping over the apples in the center and brush the pastry with the egg wash.
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Bake for 50 minutes or until golden brown.
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Let cool slightly, then serve with vanilla ice cream drizzled with reserved pan juices and maple syrup.
