Combine the flour, sugar and white vinegar and ½ teaspoon of salt in a bowl. Use your hands or a food processor to cut in the cold coconut oil until the pieces are pea size.
Add ½ cup ice water and mix one last time. If the dough holds together when squeezed in a fist it is done otherwise add 1-2 tablespoons of water.
Divide dough into two pieces and wrap with plastic wrap. Letting the dough rest in the fridge will make it easier to roll out.
Peel and core the apples and cut into 1/2-inch-thick slices. Toss with the sugar and apple cider vinegar in a large bowl. Dissolve the coconut oil in a big skillet over medium-high heat.
Now add the apples and cook, stirring intermittently, till the firmer apples soften yet hold their shape, for approximately 12 minutes. Combine the cinnamon, flour, and 1/4 teaspoon salt, and stir to mix.
Remove from heat, and let it cool completely.
Remove the dough from the fridge and roll between two rounds of floured parchment. Place into the pie pan with overhanging dough on the sides.
Add the cooled filling and top with the second piece of rolled dough. To finish the pie, fold the overhanging dough underneath itself and crimp or decorate with a fork.
Brush the top with almond or soy milk and sprinkle with sugar. Cut the top to let steam escape and put back in the fridge to chill for an hour.
Position an oven rack in the lowest point in the oven, put a baking sheet on the rack and preheat to 425 degrees F; preheat for about 30 minutes.
Place the pie on the heated baking sheet, and reduce the oven to 375 deg. F. Bake till the pie is golden and the filling is bubbling, 1 hour to 1 hour and 20 minutes, turning as needed (if the edges brown too quickly cover those with foil)