3 pounds apples mixed (such as Golden Delicious, McIntosh and Pink Lady)
2 large eggs
1 tablespoon flour all-purpose
2.5 cups flour for dusting all-purpose plus more
0.5 teaspoon ground cinnamon
1 pinch ground cloves
2 tablespoons juice of lemon fresh
1 pinch nutmeg freshly grated
1 teaspoon salt
0.3 cup sugar plus more for sprinkling
0.7 cup sugar
1 stick butter unsalted cold cut into 1/2-inch pieces
6 tablespoons butter unsalted
0.3 cup vegetable shortening
Equipment
food processor
bowl
frying pan
baking sheet
baking paper
oven
knife
plastic wrap
aluminum foil
Directions
Prepare the filling: Peel, halve and core the apples.
Cut each half into 6 wedges and toss with the sugar and lemon juice in a bowl. Melt 4 tablespoons butter in a large skillet over medium-high heat.
Add the apple mixture and cook, stirring occasionally, until the firmer apples begin to soften but still hold their shape, 8 to 9 minutes.
Sprinkle with the flour, cinnamon, cloves and nutmeg and toss until the juices begin to thicken, about 1 minute.
Remove from the heat and cool completely. (The filling can be made up to 2 days ahead; cover and refrigerate.)
Make the dough: Pulse the flour, sugar and salt in a food processor until combined.
Add the shortening and pulse until it disappears, about 30 seconds.
Add the butter and pulse until the mixture looks like coarse meal with pea-size bits of butter. Beat 1 egg with 1/4 cup ice water in a bowl, then add to the processor and pulse once or twice. (Stop before the dough gathers into a ball.)
Lay out 2 sheets of plastic wrap; divide the dough between the sheets and pat each into a disk. Wrap the disks tightly and refrigerate until firm, at least 1 hour.
Roll 1 disk of dough into a 12-inch round on a floured surface (or between 2 pieces of floured parchment paper). Ease into a 9 1/2-inch deep-dish glass pie plate.
Add the filling, mounding it slightly, and dot with the remaining 2 tablespoons butter. Chill the pie while you roll the remaining dough into a 12-inch round.
Lay the dough over the filling and press the 2 crusts together around the edges. Fold the overhanging dough under itself and crimp with your fingers. Beat the remaining egg in a bowl and brush over the top crust; sprinkle with sugar. Pierce the top with a knife a few times to let steam escape. Chill 30 minutes.
Preheat the oven to 375 degrees F.
Place the pie on a baking sheet; bake until the crust is golden and the filling is bubbly, 55 to 60 minutes. (Cover the edges with foil if they brown too quickly.)