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Step 1
Preheat an oven to 350°F (180°C).
Step 3
To make the pie crust, in a medium bowl, whisk together the almond flour, arrowroot starch and salt. Using a wooden spoon, mix in the maple syrup and vanilla bean paste until crumbly. Mix in the coconut oil, breaking up the larger pieces with the spoon, and continue to mix until pea-size crumbles form. Gather the dough into a ball, then transfer to a work surface and flatten into a disk. Wrap in plastic wrap and refrigerate until ready to use, up to 3 days.
Step 5
To make the filling, in a large bowl, stir together the apples, lemon juice, maple sugar, cinnamon and salt.
Step 7
Heat a 10-inch (25-cm) ovenproof fry pan over medium heat and warm 1 Tbs. of the coconut oil. Add half of the apple mixture and cook, stirring frequently, until the apples are tender, about 8 minutes. Add 1 Tbs. of the arrowroot starch and stir to combine. Transfer to a large bowl. Heat the remaining 1 Tbs. coconut oil in the pan and cook the remaining apple mixture, then stir in the remaining 1 Tbs. arrowroot starch. Transfer to the bowl and stir to combine, then return the apple mixture to the pan and spread in an even layer.
Step 9
While the apples are cooking, place the dough disk between 2 sheets of parchment paper. Using a rolling pin, roll out the dough about 1/4 inch (6 mm) thick. If it tears in places, just continue rolling.
Step 11
To assemble the pie, break the dough into 2-inch (5-cm) pieces and arrange like a mosaic evenly over the top of the apple mixture, covering it completely and overlapping the pieces as needed. Place any remaining dough pieces on top. Gently press the dough down to make it look more cohesive. Sprinkle the top with the turbinado sugar.
Step 13
Bake until the crust is slightly caramelized, 25 to 30 minutes. Transfer the pan to a wire rack and let cool for 10 minutes; this will allow the crust to set. Cut the pie into slices and serve with dairy-free vanilla ice cream. Serves 6 to 8.
Step 14
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