1. For the pastry, combine flour, 1 tablespoon granulated sugar and salt in a food processor and pulse to combine. Add butter and pulse until mixture resembles coarse crumbs. Whisk together egg yolk and vinegar in a cup. Sprinkle yolk mixture onto flour mixture; pulse to combine. With machine running, gradually add half and half cream through feed tube, pulsing just until pastry holds together. Shape into 2 balls, one slightly larger than the other; flatten into thick disks. Wrap well in plastic wrap and refrigerate 30 minutes or overnight.
2. Arrange rack in lower third of oven. Heat oven to 375 degrees F.
3. For the filling, meanwhile, divide apples into each of 2 shallow 4-quart glass baking dishes. Sprinkle 1/4 cup granulated sugar over apples in each dish. Cover tightly with foil. Bake apples about 45 minutes, or until partially tender (apples should still hold their shape). Cool on wire rack, covered, 30 minutes.
4. Lightly coat a 10-inch pie plate with vegetable cooking spray. On a lightly floured surface with a floured rolling pin, roll larger pastry disk into a 15-inch circle. Fit into pie plate, leaving a 1-inch overhang. Beat egg white with water in a cup; brush pie shell with about 2 teaspoons egg-white mixture, then set aside to dry.
5. Heat oven to 375 degrees F. Combine remaining 1/2 cup granulated sugar, the brown sugar, apple pie spice, cornstarch and salt in a bowl. Spoon one third of apples and juices into the pie shell; sprinkle with one third of the sugar mixture. Drizzle filling with 1 teaspoon lemon juice and dot with one third of the butter. Repeat layering 2 more times with remaining apples, sugar mixture, lemon juice and butter.
6. Roll remaining pastry into a 13-inch circle. Place over filling; cut vents in top and flute edge. Brush top with 2 teaspoons of egg-white mixture, then with the 2 tablespoons heavy cream and sprinkle with the 1 teaspoon granulated sugar.
7. Place pie on a foil-lined cookie sheet. Bake 1 hour 15 minutes, or until crust is golden brown and filling is bubbly. (If crust browns too quickly, cover top loosely with foil.) Cool on a wire rack. Serve warm or at room temperature.