2 tablespoons all-purpose flour, plus more for dusting
12 Granny Smith apples, peeled, cored, and sliced
3/4 cup sugar, plus additional for pie top
Zest and juice of 1 lemon
1 1/2 teaspoons cinnamon
1/2 teaspoon nutmeg
Pinch ground cloves
2 tablespoons unsalted butter
1 large egg, beaten
Heat oven to 375 degrees. On a lightly floured surface, roll out pate brisee into two 1/8-inch-thick circles to a diameter slightly larger than that of an 11-inch plate. Press one pastry circle into the pie plate. Place the other circle on waxed paper, and cover with plastic wrap. Chill all pastry until firm, about 30 minutes.
In a large bowl, combine apples, sugar, lemon zest and juice, spices, and flour. Toss well. Spoon apples into pie pan. Dot with butter, and cover with remaining pastry circle. Cut several steam vents across top. Seal by crimping edges as desired. Brush with beaten egg, and sprinkle with additional sugar.
Bake until crust is brown and juices are bubbling, about 1 hour. Let cool on wire rack before serving.