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Preheat oven to 375 degrees F.
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Peel apples and slice to ⅛ - ¼” thickness.
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In bowl, toss apples with cinnamon, maple syrup, salt and egg replacer. Set aside.
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In large bowl, sift together flour and salt. Using fork, blend coconut oil and water into dough. Knead dough thoroughly. Divide in half.
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On flat, floured surface using rolling pin, roll half of dough into a 12-inch circle. Fold crust in half, place in pie plate, then unfold and adjust dough to fit plate and onto rim.
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Pour in filling ingredients.
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Roll out second half of dough for lattice topping. Using pizza cutter, cut ½-¾-inch strips, creating 12 total. Arrange 6 strips across top, side by side and evenly spaced. (Note: Use longer strips in middle and shorter strips toward edges of pie.)
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Position pie in front of you with dough strips facing away. Carefully fold back – all the way toward you – the second, fourth and sixth strips, then lay strip of dough perpendicularly across first, third and fifth strip near edge of pie closest to you.
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Unfold second, fourth and sixth strips over new strip.
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Fold back the first, third and fifth strips toward you, then lay another strip of dough perpendicularly across pie. Unfold first, third and fifth strips over new strip.
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Repeat steps 8, 9 and 10 until pie is fully covered with lattice crust.
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Trim dough strips overhanging pie plate: fold under edges to create a border that rests on rim.
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Place pie plate on baking sheet. Bake 40-45 minutes, checking the last 10 minutes for golden-brown crust and doneness of apples.
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Cool to room temperature before serving.