Sift flour into a large bowl. Rub in butter with your fingers until mixture resembles fine crumbs. Stir in sugar, vanilla, cold water, and baking powder until a firm dough forms.
Knead dough gently and briefly on a floured work surface. Wrap in plastic wrap and let chill, about 30 minutes.
Place apples in a pot and cover with water. Bring to a boil; reduce heat and simmer gently until soft, 15 to 20 minutes. Drain. Mash with a hand blender or potato masher into a thick puree; let cool.
Preheat oven to 400 degrees F (200 degrees C). Grease a 9-inch pie plate.
Press 2/3 of the dough into the pie plate evenly with your fingers to make the crust. Prick crust all over with a fork.
Bake crust in the preheated oven until golden, about 20 minutes.
Grate remaining 1/3 of the dough onto a baking sheet to make crumbles.
Bake crumbles in the preheated oven until golden, about 10 minutes. Reduce oven temperature to 200 degrees F (95 degrees C).
Place aquafaba and cream of tartar in the bowl of a stand mixer fitted with a whisk attachment. Beat on high, gradually adding confectioners' sugar, until meringue is stiff and glossy, 10 to 15 minutes.
Measure out 1 1/4 cup apple puree into a bowl. Stir in cinnamon. Spread apple-cinnamon puree over cooled pie crust. Spread meringue over the puree.
Bake pie in the preheated oven until golden, 60 to 90 minutes. Turn off oven; keep pie inside until cooled, 45 minutes to 1 hour.