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1
Make the dough: In a food processor combine the flour and salt.
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2
Add the butter and shortening and pulse until it resembles very coarse meal.
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3
Add the Cheddar and pulse until it again resembles coarse meal.
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4
Transfer the mixture to a bowl.
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5
Add the yolk mixture, tossing with a fork until it forms a dough.
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6
Add more cold water 1 tablespoon at a time, if necessary.
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7
Form the dough into a ball, flatten it into a disc, and dust with flour.
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8
Wrap the dough in waxed paper and chill for at least 1 hour or overnight.
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9
Roll out half the dough 1/8-inch thick on a lightly floured surface.
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10
Fit it into a 9-inch (1-quart) glass pie plate and trim the edge, leaving a 3/4-inch overhang.
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11
Chill the shell and the remaining dough while making the filling.
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12
Make the filling: Preheat the oven to 450 degrees.
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13
Peel, core, and cut the apples into eighths.
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14
In a large bowl toss together the apples, 3/4 cup of the sugar, the flour, the cinnamon, the nutmeg, the salt, and the lemon juice until the mixture is combined well.
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15
Transfer the filling to the shell and dot it with the butter.
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16
Roll out the remaining dough into a 13- by 14-inch round on a lightly floured surface, drape it over the filling, and trim it, leaving a 1-inch overhang.
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17
Fold the overhang under the bottom crust, pressing the edge to seal it, and crimp the edge decoratively.
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18
Brush the crust lightly with the milk and cut slits in it with a sharp knife to form steam vents.
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19
Bake the pie on a large baking sheet in the middle of the oven for 10 minutes.
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20
Reduce the temperature to 350 degrees and bake the pie for 20 to 25 minutes more, or until the crust is golden and the apples are tender.
