1. In a large bowl, combine 4 cups of flour, 1 teaspoon of sugar and the pinch of salt. Use a pastry blender to cut in the butter until the mixture feels like coarse crumbs.

2. Add one tablespoon of water at a time to moisten it, and mix, repeating until a dough starts to form.

3. Knead the dough into a ball, then divide in half, flatten each half into a rectangle and wrap in plastic wrap. Refrigerate for at least 2 hours.

4. Combine the apples in a large bowl with cinnamon, remaining ⅓ cup of flour, and ½ cup of sugar. Toss until the apples are coated and allow to sit until the apples release their excess juices.

5. Preheat the oven to 350 degrees. Spray a half sheet pan (15 x 10 x 1) with non-stick cooking spray.

6. Lightly flour a work surface and roll one piece of the dough into a 19x13 rectangle. Place the dough onto the prepared pan and gently press it up the sides, being careful not to make the dough too thin in the center. Trim any excess dough and set aside. Crimp the edges or press down to smoothen.

7. Remove the apples from the bowl with a slotted spoon, allowing any excess juices to drain back into the bowl. Spread the apples over the dough in an even layer.

8. On a lightly floured surface, roll out the remaining piece of dough and any excess into a rectangle. Use leaf shaped cookie cutters to cut out dough leaves. (Alternately or in addition, use a pizza cutter to cut the dough into strips for a lattice top.)

9. Arrange the dough leaves or strips over the apples, leaving areas where the apples are still visible so the steam can escape while cooking.

10. Brush the whisked egg over the leaves and edges of the dough.

11. Bake for 40-45 minutes or until the apples are fork tender and the dough is golden brown. Cut into squares and serve, optionally topped with vanilla ice cream.