Apple–Brown Sugar Pie

Name: Apple–Brown Sugar Pie
Ingredients: 1½ teaspoons kosher salt; 2¾ cups all-purpose flour, plus more; 14 tablespoons (1¾ sticks) chilled unsalted butter, cut into pieces; ⅓ cup chilled shortening, cut into pieces; 4 pounds Granny Smith apples, peeled, sliced into ½-inch wedges; 1 cup plus 2 tablespoons granulated sugar; ¼ cup plus 1 heaping tablespoon all-purpose flour, plus more; ½ cup (1 stick) unsalted butter, cut into pieces, room temperature; ½ cup (packed) light brown sugar; 1 teaspoon ground cinnamon; 1 large egg, beaten to blend; Lightly sweetened crème fraîche or whipped cream (for serving)