In a large bowl, whisk together the gluten-free flour, sugar, and salt.
Add the cold cubed vegan butter, using a pastry cutter or two forks to cut it into the flour until the mixture resembles coarse crumbs with pea-sized pieces remaining.
Mix the ice-cold water and apple cider vinegar in a small cup. Add the liquid to your flour mixture one tablespoon at a time, gently mixing until the dough just comes together. Be careful not to overwork it.
Form the dough into two equal discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Peel, core, and slice your apples into ¼-inch thick slices. Toss apple slices with lemon juice to prevent browning.
In a large bowl, mix sugar, cornstarch, cinnamon, nutmeg, cardamom, and salt. Add the apples and vanilla, gently tossing until evenly coated. Set aside to macerate for 15 minutes.
Preheat your oven to 375°F (190°C) and place a baking sheet on the middle rack.
Remove one disc of dough from the refrigerator and let it sit for 5 minutes to slightly soften. On a lightly floured piece of parchment paper, roll the dough into a 12-inch circle about ⅛-inch thick.
Carefully transfer to a 9-inch pie dish, gently pressing into the bottom and sides. Trim any excess, leaving about a ½-inch overhang.
Pour the apple filling into the crust, making sure to include all the juices. Dot with the remaining 2 tablespoons of vegan butter pieces.
Roll out the second disc of dough just like the first. You can either place it whole over the filling for a traditional pie, or create a lattice pattern. If using a whole crust, make sure to cut several slits for steam to escape.
Trim excess dough, then fold and crimp the edges to seal.
If desired, brush the top crust lightly with a mixture of non-dairy milk and maple syrup for a golden finish. Sprinkle with coarse sugar if desired.
Bake for 20 minutes at 375°F, then reduce temperature to 350°F (175°C) and continue baking for 30-35 minutes more, until the crust is golden and the filling is bubbling. Cover the edges with foil if they brown too quickly.
Allow your pie to cool for at least 3 hours before serving to allow the filling to set properly.