"THE CRUSTRefrigerate the butter, shortening and applejack for 1 hour.Combine the flour, salt and sugar in your food processor by pulsing 3 or 4 times. Add the butter and pulse 5 or 6 times, until the texture looks mealy. Add the shortening and pulse another 3 or 4 times, until incorporated.Pop off the lid and sprinkle in 5 tablespoons of the applejack. Replace the lid and pulse 5 times. Add more applejack as needed until the mixture holds together when squeezed. Weigh the dough and divide it in half. Shape each half into a disk, wrap in plastic wrap and refrigerate for at least 1 hour or up to overnight.THE FILLINGPeel and core the apples and slice into 1/2-inch-thick wedges). Toss apples with 1/4 cup of the sugar, place in a colander set over a large bowl, and drain for 1 1/2 hours.Transfer the drained liquid to a small saucepan, place over medium heat and cook until it is reduced down to a mere 2 tablespoons then set aside to cool. Toss the apples with the remaining sugar, the tapioca flour, jelly, cider, lime juice, salt and grains of paradise.Heat oven to 425 degrees F.Remove one disk of dough from the refrigerator. Place the dough on a lightly floured piece of waxed paper or parchment paper. Lightly sprinkle the top of the dough with flour and roll out into a 12-inch circle. Place in a 9 1/2- to 10-inch tart pan that is 2 inches deep. Gently press the dough into the side of the pan, crimping and trimming the edges as necessary. Set a pie bird in the center of the bottom of the pan. (If you’ve got one it really will help to vent steam out of the pie. If you don’t have one, you can skip it but…your pie won’t be quite as solid inside.)Arrange the apples in the unbaked pie shell in concentric circles starting around the edges, working toward the middle and forming a slight mound in the center of the pie. Pour any liquid that remains in the bowl over the apples.Roll out the second disk of dough as the first. Place this dough over the apples, pressing the pie bird through the top crust. Press together the edges of the dough around the rim of the pie. Brush the top crust with the reduced juice everywhere except around the rim of the pie. Trim off any excess dough.Place the pie on a half sheet plan lined with parchment paper and bake on the floor of the oven for 30 minutes. Transfer to the lower rack of the oven and continue to bake for another 20 minutes, or until the apples are cooked through by not mushy. Remove to a rack and cool at least 4 hours before serving. And by the way, ice cream won’t really improve this pie, but whipped cream is OK by me."