Preheat oven to 375F. Line a pie plate with one pie crust, gently pressing dough into sides, and letting excess hang over the edge.
In a large bowl, combine apples, flour, sugar, cinnamon, nutmeg, lemon juice, vanilla and salt. Spoon into pie crust and scatter bits of butter evenly over filling. Top with an even layer of cheese.
Drape second crust loosely over filling. Pull excess from the bottom crust over edge of top crust and crimp to enclose. Flute edge decoratively. Brush top crust lightly with beaten egg and use a sharp knife to make 4 to 5 small (1/2-inch) slits.
Bake until top is golden brown and fruit is bubbling and tender, about 50 to 55 minutes. If crust browns too quickly, drape pie lightly with foil and continue cooking.