How to Make It
Prepare the Crust: Pulse flour, sugar, and salt in a food processor 3 to 4 times. Add butter; pulse until mixture resembles coarse meal, 8 to 10 times. Drizzle 4 tablespoons of the cold water over flour mixture; pulse until moist clumps just form, 4 to 5 times. If needed, add up to remaining 1 tablespoon water 1 teaspoon at a time, pulsing 1 to 2 times after each addition, until mixture clumps. Gather into a ball; flatten into a disk. Wrap in plastic wrap; chill dough 30 minutes or up to 3 days.
Place a rimmed baking sheet in oven; preheat oven to 400°F. Unwrap chilled dough disk. Roll dough into a 12-inch circle (about 1/8 inch thick) on a lightly floured surface. Fit into a 9-inch pie plate. Fold edges under; crimp. Prick bottom and sides using a fork. Line dough with parchment paper; fill with pie weights or dried beans. Bake on hot baking sheet 20 minutes.
Whisk together egg white and 1 teaspoon tap water in a bowl. Remove Crust from oven (leave baking sheet in oven). Place Crust on a wire rack; remove pie weights and parchment. Let stand 1 minute. Brush bottom and sides with egg mixture. Return to oven (on baking sheet); bake at 400°F for 5 minutes. Place Crust on wire rack; cool completely, 30 minutes.
Prepare the Filling: Reduce oven temperature to 350°F. Spread oats on rimmed baking sheet. Bake, stirring occasionally, until toasted, 10 to 12 minutes. Transfer baking sheet to a wire rack; cool about 10 minutes.
Reduce oven temperature to 325°F. Stir together chocolate and heavy cream in a small microwavable bowl. Microwave at MEDIUM (50%) power until melted and smooth, 1 1/2 to 2 minutes, stopping to stir every 30 seconds. Pour mixture into cooled Crust; spread in an even layer. Freeze until ganache is firm, about 10 minutes.
Whisk together brown sugar, melted butter, cocoa, salt, and ginger in a medium bowl. Whisk in cane and corn syrups, vanilla, and vinegar. Add eggs 1 at a time, whisking well after each addition. Stir in cooled oats until well combined. Remove Crust from freezer, and pour in Filling.
Bake on baking sheet at 325°F until edges are set and center is firm to the touch, 50 to 55 minutes, covering edges with aluminum foil after 30 to 35 minutes, if needed. Transfer to a wire rack; cool completely, about 3 hours.