Make the crust: In a food processor or mixer fitted with a paddle attachment, combine flour and salt. Add butter one piece at a time, while pulsing or mixing at low speed, until mixture is fine and crumbly. Transfer to a large bowl and toss well with the cheese. Add ice water one tablespoon at a time, mixing lightly with fingers just until dough holds together. To test, pinch a small amount of dough. If it is crumbly, add more ice water. Form dough into a ball, wrap loosely in plastic, then roll into a disk. Refrigerate at least one hour, or up to 3 days, before rolling. (Dough can be frozen for up to a month.)

On a lightly floured surface, roll dough into a circle at least 11 inches in diameter. Transfer to a 9-inch pie pan, preferably glass. Turn edges under to make a thick rim; flute rim by pinching into a zigzag pattern. Refrigerate until ready to bake, at least an hour.

Make the filling: In a large bowl, toss apples, green chilies and lemon juice together. In another bowl, mix dry ingredients and add to apples and chilies, tossing until thoroughly coated.

Bake the pie: Heat oven to 400°F. Using a slotted spoon, scoop filling into chilled crust, then drizzle with 2 tablespoons of juice from bottom of bowl. Sprinkle topping evenly over filling. Bake 10 minutes, then reduce heat to 375°F. Bake 30 to 40 minutes, or until filling bubbles at edge and crust is brown. Serve warm, with a scoop of vanilla ice cream on the side.