Peel and core the apples, setting aside the peels to make a stock. As soon as the apples are peeled, immerse them in a large bowl of water with the juice of 1 lemon dissolved in it. Slice them into wedges, about the size of an orange section. Return them to the water immediately to prevent discoloration. You should get about 5 cups.
To make apple stock: In a small pot, combine the apple peels with 2 cups of water. Place over a high heat and bring to a boil. Reduce the heat to medium and simmer for about 15 minutes. Drain and reserve the stock.
Dissolve the cornstarch in the water.
Melt the butter in a 4-quart pot over high heat until the butter begins to sizzle. Add the cinnamon and the Anaheim, Ancho and New Mexico chiles and whisk constantly for 2 minutes. Add the sugar and 1 cup of the apple stock. Cook for 2 minutes, whisking constantly, then add the cane vinegar and vanilla. Cook, whisking frequently until the mixture begins to reduce, about 5 minutes. Add the cornstarch mixture and whisk constantly and quickly until the mixture is evenly distributed and the liquid on the pot has thickened to the consistency of a very thick gravy. Add the cheese and whisk in thoroughly until dissolved. Add the apples and currants. Stir until they are all coated evenly with the mixture. Cover the pot, reduce the heat to medium low and cook for 5 more minutes, then remove from heat.
Preheat the oven to 350ºF.
Make the Chili Pie Crust.
Roll out the pie dough to about ¼-inch thickness, being sure that your work surface and the dough are well floured. Line a 9-inch pie tin with the dough, saving the scraps for use later. Fill the pie shell with the apple mixture and cover the pie with a lattice or other decorative shapes made from the scraps.
Bake in a preheated oven for 45 minutes, or until the crust is golden. Cool to room temperature, then refrigerate until cold. For best flavor and easy cutting, be sure that this pie is well chilled.
NOTE: Pie tins vary considerably in size and capacity. So if you have too much filling for your pie, remove some of the liquid so that the level falls slightly below the top of the pie crust.
NOTE:This pie can also be prepared in a conventional pre-baked pie shell.