Chill the very cold unsalted butter for about 15 minutes. In a mixing bowl, combine whole wheat pastry flour and fine sea salt. Cut in the chilled butter using a pastry cutter until the mixture resembles small peas. Gradually drizzle in ice water and apple cider vinegar, mixing gently until a dough forms. Shape into a disc, wrap in plastic, and chill for 2 hours.

Peel and slice the apples into thin wedges. In a large bowl, toss the apple slices with brown sugar, tapioca flour, ground cinnamon, vanilla extract, and lemon juice. Let the filling sit for 20-30 minutes.

Roll one disc of dough into a 12-inch circle, ensuring it’s about 1/8 inch thick. Transfer it to a 9-inch pie dish, pressing it into the bottom and sides. Trim any overhanging edges and refrigerate the crust.

Layer the prepared apple filling into the crust, drizzling any reserved juices over the top.

Roll out the second disc of dough into a 12-inch circle, cut it into ¾-inch strips, and weave these strips over the filled pie. Brush the lattice with a mixture of beaten egg and milk.

Preheat the oven to 400ºF (200ºC). Bake for 20 minutes, then lower the temperature to 375ºF (190ºC). Cover the pie's edges with foil and bake for an additional 30-35 minutes.

Allow the pie to cool for at least 3-4 hours before serving.