Apple Pie

INGREDIENTS

6 oz

unsalted butter, cut into 1/2-inch pieces

2 oz

vegetable shortening, cut into 1/2-inch pieces

to 7 tablespoons applejack or apple brandy (calvados)

12 oz

all-purpose flour, plus extra for dusting

1 tsp

table salt

1 tbsp

granulated sugar

4 1/2 lb

peeled and seeded apples from a mix of Granny Smith, Honeycrisp, Braeburn and Golden Delicious, about 8 large apples

1/2 cup

sugar, divided

3 tbsp

tapioca flour

2 tbsp

apple jelly

1 tbsp

apple cider

2 tsp

lime juice, freshly squeezed

1/4 tsp

kosher salt

1/4 tsp

grains of paradise, freshly ground (see note)