1. Have a 9-inch pie pan on hand.
2. In a bowl, combine the flour, nutmeg, and salt. Scatter the butter on top. Using two blunt knives or a pastry blender, cut the fat into the flour until the mixture resembles crumbs. Stir in the sugar.
3. In a small bowl, combine yolk and water. Pour them over the flour mixture and mix with one of the blunt knives to form a dough.
4. Press the dough into a rough cake and wrap it in waxed paper. Refrigerate for 10 minutes.
5. Cut 2 14-inch pieces of waxed paper. Roll the dough between the sheets to a 10 1/2-inch round (it will be 1/8-inch thick). Peel off the top paper and invert the dough onto the pie pan. Peel off the second sheet of paper. Press the dough lightly into the bottom and sides of the pan. Tuck under the excess dough around the rim and press it. Flute the edges. Refrigerate for 2 hours.
1. In a bowl, combine the flour, cinnamon, nutmeg, and salt. Stir in the brown and granulated sugar.
2. Scatter over the butter on top. With 2 blunt knives or a pastry blender, cut the butter into the flour mixture until reduced to small pieces. With your fingertips, knead to form moist crumbs.
1. Set the oven at 425 degrees. Place a rimmed baking sheet or jelly roll pan in the oven 5 minutes before baking.
2. With a fork, lightly prick the bottom of the chilled dough without going all the way through. Cover the dough with foil, fill it with raw rice or beans, and transfer the pan to the hot baking sheet.
3. Bake the dough for 10 minutes. Lift off the foil.
4. Lower the oven temperature to 375 degrees. Continue baking the dough for 10 minutes or until pale golden.
5. Paint the inside of the crust with the reserved egg white. Return the crust to the oven and bake for 2 minutes. Transfer to a cooling rack. Leave the sheet pan in the 375 degree oven.
6. In a large bowl, combine the granulated and brown sugar, cornstarch, cinnamon, nutmeg, and salt. Add the apples and toss.
7. Mound the filling in the warm crust. Sprinkle with the crumb topping.
8. Place the pie on the hot baking sheet and bake for 60 to 65 minutes or until the apples are tender and the juices bubble up. Time depends on the juiciness of the apples; test them with a toothpick. After 60 minutes, if the pie needs to be baked longer, gently cover the top with a sheet of foil.
9. Cool on a rack and serve warm.