Heat oven to 400°F.
Place 1/2 cup cold butter and 5 slices cheese into food processor bowl fitted with metal blade. Pulse until cheese and butter are well mixed. Add 2 cups flour and salt. Process until mixture resembles coarse crumbs. With processor running, add 1 tablespoon water at a time, just until dough forms ball.
Divide dough in half; shape each half into ball. Flatten slightly. Wrap 1 ball dough in plastic food wrap; refrigerate. Roll out remaining dough, on lightly floured surface, into 12-inch circle. Place dough into 9-inch glass pie pan, pressing firmly against bottom and sides. Trim crust to 1/2 inch from edge of pan. Lay cheese evenly over bottom crust. Cover loosely with plastic food wrap; set aside.
Combine 1/3 cup sugar, brown sugar, 3 tablespoons flour and cinnamon in bowl. Add apples; toss to coat. Spoon apple mixture into prepared crust.
Roll out remaining dough, on lightly floured surface, into 12-inch circle. Fold into quarters. Place dough over filling; unfold. Trim, seal and crimp or flute edge. Cut 5 or 6 large slits in crust. Brush with melted 1 tablespoon butter; sprinkle with 1 teaspoon sugar. Cover edge of crust with 2-inch strip of aluminum foil.
Bake 35 minutes; remove aluminum foil. Continue baking 10-12 minutes or until crust is lightly browned and juices begin to bubble through slits in crust. Cool 30 minutes; serve warm. Store refrigerated.