1. For the pastry, combine flour, 1 tablespoon granulated sugar, and 1 teaspoon 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. With machine running, gradually add cream through feed tube, pulsing until pastry holds together. Shape into 2 balls, one slightly larger than the other; flatten into disks.
2. For the filling, heat oven to 375 degree F. Divide apples into each of 2 shallow 4-quart glass baking dishes. Sprinkle 1/4 cup granulated sugar over each dish. Cover tightly with foil. Bake apples about 45 minutes, or until partially tender (apples should still hold their shape). Cool, covered, 30 minutes.
3. On light floured surface, roll larger pastry disk into a 15-inch circle. Fit into 10-inch pie plate, leaving 1-inch overhang. Beat egg white with water in cup; brush pie shell with about 2 teaspoons, then set aside to dry.
4. Heat oven to 375 degree F. Combine remaining 1/2 cup granulated sugar, brown sugar, apple pie spice, cornstarch and 1/4 cup salt in 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 3 tablespoons butter. Repeat layering 2 more times with remaining apples, sugar mixture, lemon juice, and butter.
5. Roll remaining pastry into a 13-inch circle. Place over filling; cut slits in top. Flute edge. Brush top with 2 teaspoons of egg-white mixture, then with cream and sprinkle with sugar.
6. Place pie on foil-lined baking 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. Makes 10 servings.