MAKES: one 9-inch pie
3 pounds mixed apples (such as Granny Smith, Gala and McIntosh)
2/3 cup granulated sugar
2 tablespoons fresh lemon juice
6 tablespoons unsalted butter
1 tablespoon all-purpose flour, plus more for dusting
3/4 teaspoon ground cinnamon
1/8 teaspoon salt
2 disks dough for Basic Crust
1 large egg, beaten
Coarse sugar, for sprinkling
Peel and core the apples; slice 1/4 inch thick. Toss with the granulated sugar and lemon juice. Heat 4 tablespoons butter in a large skillet over medium-high heat. Add the apples and cook, stirring, until tender, about 10 minutes. Stir in the flour, cinnamon and salt; cook until thickened, 1 more minute. Let cool.
Roll out 1 disk of dough into a 12-inch round on a floured surface; ease into a 9-inch pie plate. Add the apples, mounding them slightly in the center, and dot with the remaining 2 tablespoons butter. Roll out the remaining dough into a 12-inch round. Lay it over the filling; press the edges of the crusts together, then fold the overhang under itself and crimp to seal. Brush with the beaten egg and sprinkle with coarse sugar. Cut a few slits in the top crust. Chill 1 hour.
Place a baking sheet on the lowest oven rack and preheat to 425 degrees F for 30 minutes. Place the pie on the hot baking sheet; lower the temperature to 375 degrees F. Bake until golden, 1 hour to 1 hour, 10 minutes. (Cover the edges with foil if they brown too quickly.) Cool on a rack.
2. Apple-Berry Make Apple Pie, adding 1 extra tablespoon flour and 1 teaspoon vanilla to the filling. Off the heat, stir in 1 cup mixed berries. Top with a lattice crust, brush with a beaten egg and sprinkle with coarse sugar.
3. Apple-Cheddar Make Apple Pie, adding 2/3 cup diced sharp cheddar to the cooled filling before baking.
4. Tart Apple Make Apple Pie with very thinly sliced Granny Smith apples; toss with apple cider instead of lemon juice. Don't cook the filling. Omit the 4 tablespoons butter; toss with 2 extra tablespoons flour, the cinnamon, salt and 1/2 teaspoon nutmeg.
5. Apple Crumble Make Apple Pie, adding 1 extra tablespoon flour to the filling. Off the heat, add 1/2 cup sour cream and 1/2 teaspoon nutmeg. Omit the top crust. Mix 1/2 cup flour, 1 cup oats, 3/4 cup each chopped walnuts and brown sugar, 6 tablespoons melted butter and a pinch of salt. Drop in clumps over the filling.
6. Apple Strudel Make Apple Pie with grated peeled Golden Delicious apples. Don't cook the filling. Omit the 4 tablespoons butter; toss the apples with the cinnamon, salt, 2 extra tablespoons flour and 1/2 cup raisins. Dot with 1 extra tablespoon butter.
7. Apple-Pear-Ginger Make Apple Pie, replacing half of the apples with pears and using ground ginger instead of cinnamon. Cut the top crust into decorative shapes; arrange on top of the filling. Brush with a beaten egg and sprinkle with coarse sugar.
8. Apple-Fig Combine 1 1/2 pounds sliced peeled apples, 1/2 pound each dried apples and figs, 1/8 cup sugar, 2 tablespoons lemon juice and 1/2 teaspoon cinnamon in a food processor; finely chop. Don't cook the filling. Assemble as for Apple Pie, dotting with 2 extra tablespoons butter. Bake 50 minutes.
9. Salted Caramel Apple Toss 3 pounds sliced peeled apples with 2 tablespoons lemon juice. Cook 2/3 cup sugar over medium-high heat until amber, about 10 minutes. Off the heat, stir in 1/2 stick butter and 1 tablespoon cream. Add the apples and cook until soft. Stir in 2 tablespoons flour; let cool, then add 1/2 teaspoon sea salt. Assemble and bake as for Apple Pie.
10. Hazelnut-Apple Crumble Make Apple Pie, using chopped McIntosh and Cortland apples. Omit the top crust. Mix 1/2 cup flour, 1 cup oats, 3/4 cup each brown sugar and chopped hazelnuts, 6 tablespoons melted butter and a pinch of salt. Drop in clumps over the filling.