Preheat the oven to 300°F. Lightly spray a 9-inch pie pan with oil. Grind the cookies to a powder in a food processor. Sprinkle with half the cookie crumbs and set aside. Stir together 1/3 cup of the sugar and the cocoa, and set aside.

Beat the egg whites in an electric mixer at low speed 1 minute. Add the cream of tartar. Gradually increase the speed and beat the whites to soft peaks. Add the remaining 1/3 cup sugar in a thin stream and continue beating until the whites are firm and glossy but not dry. Stir in the vanilla. Using a rubber spatula, fold in the cocoa mixture as gently as possible. Spoon the meringue into the crumb-lined pie pan, spreading it across the bottom and up the sides.

Bake the meringue until crisp, 1-1/2 to 2 hours. Transfer the pan to a wire rack to cool.

Meanwhile, prepare the Intense Chocolate Pudding. Spoon the cooled pudding into the meringue shell and sprinkle with the remaining cookie crumbs.