Preheat oven to 350°. Position rack in lower third of oven.
In a medium bowl, whisk together sugars, flour, cornstarch, cinnamon, salt, ginger, allspice, and nutmeg.
In a large bowl, toss apples with lemon juice and vanilla. Add sugar mixture to apple mixture, tossing to combine. Let apples stand for at least 15 minutes.
In a Dutch oven, cook apple mixture over medium-high heat, stirring frequently, until thickened, 6 to 8 minutes. Remove from heat, and let cool completely.
On a lightly floured surface, roll half of dough into a 12-inch circle. Transfer to a 9-inch deep-dish pie plate, pressing into bottom and up sides. Fold edges under, and crimp as desired. Spoon apple mixture into prepared crust. Top with Oatmeal-Almond Crumble.
On a lightly floured surface, roll remaining dough into a 12-inch circle. Using a small leaf-shaped cutter, cut leaves from dough. Using a pastry brush, lightly brush crimped edges with egg white. Press leaves on crimped edges, overlapping slightly. Sprinkle with sparkling sugar.
Bake until crust is light golden brown and filling is bubbly, 20 to 25 minutes, covering with foil halfway through baking to prevent excess browning, if necessary. Let cool slightly. Serve warm or chilled with Calvados Crème Anglaise. Cover and refrigerate for up to 3 days.