1. To prepare crust, weigh or lightly spoon potato starch and flour into dry measuring cups; level with a knife. Combine potato starch, flour, 1 tablespoon sugar, and salt in a bowl; stir with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add milk; toss with a fork until moist. Gently press mixture into a 4-inch circle on 2 sheets of heavy-duty plastic wrap that overlap; cover with additional overlapping plastic wrap. Chill 1 hour.
2. To prepare filling, place apples, and next 7 ingredients (through nutmeg) in a large bowl; toss to combine.
3. Preheat oven to 350°.
4. Roll dough, still covered, into a 12-inch circle. Fit dough, plastic wrap side up, into a 9-inch pie plate coated with cooking spray. Remove remaining plastic wrap. Press dough against bottom and sides of pan. Fold edges under or flute decoratively.
5. Sprinkle 1/4 cup cheese over piecrust. Spoon apple mixture over cheese; top with 1 tablespoon butter pieces. Bake at 350° for 20 minutes.
6. To prepare topping, place 1/4 cup granulated sugar, 1/4 cup brown sugar, and 1/4 teaspoon salt in a food processor; process until combined. Add oats, cookies, and 4 tablespoons butter; pulse 2 times or until crumbly. Remove pie from oven; sprinkle with 1/4 cup cheese and topping, pressing gently to adhere. Bake an additional 30 minutes or until golden brown. Cool on a wire rack.