Make the cake: Preheat the oven to 350 degrees F. Coat two 8-inch-round cake pans with cooking spray and line the bottoms with parchment paper. Lightly coat the parchment with cooking spray and dust the pans with flour, tapping out the excess. Sift the flour, cornstarch, salt and pumpkin pie spice together into a medium bowl; set aside.
Beat the egg yolks and 1/2 cup superfine sugar in a large bowl with a mixer on medium speed until very thick and light in color, 3 to 5 minutes. (The yolks should fall in a thick ribbon when the beaters are lifted.) Add half of the flour mixture and fold in with a rubber spatula until just incorporated. Add the melted butter, vanilla and the remaining flour mixture and fold until the batter is smooth and elastic. Divide the batter between the prepared pans, spreading it to the edges (the layers will be thin).
Make the meringue: Beat the egg whites and cream of tartar in a separate large bowl with the mixer (and clean beaters) on medium speed until foamy, 1 to 2 minutes. Increase the speed to medium high and beat, slowly adding the remaining 1 cup superfine sugar, until stiff glossy peaks form, about 5 more minutes. Divide the meringue between the pans on top of the cake batter, spreading it to the edges; sprinkle with the almonds. Bake until the meringue is browned and crisp, 35 to 40 minutes. (The layers will puff and then collapse as they bake.) Transfer to a rack and let cool in the pans.
Meanwhile, make the filling: Put the white chocolate in a small microwave-safe bowl and microwave in 30-second intervals, stirring, until smooth and melted; set aside. Beat 2/3 cup heavy cream and 1 tablespoon superfine sugar in a medium bowl with a whisk until stiff peaks form; set aside. In a separate medium bowl, combine the cream cheese and the remaining 1 tablespoon superfine sugar with a rubber spatula; mix in the remaining 2 tablespoons heavy cream, the vanilla and nutmeg, then stir in the melted white chocolate. Fold in the whipped cream. Refrigerate until firm but not completely set, 30 to 45 minutes.
Run a thin knife around the edges of the cakes and invert onto a cutting board; peel off the parchment. Place 1 cake, meringue-side down, on a flat platter. Spread the filling on the cake, then top with the second cake layer, meringue-side up, pressing gently. (If you're not serving it right away, refrigerate up to 1 day; bring to room temperature before serving.)