In addition to being a cute, seasonal garnish for this cake, the leaf-shaped pie crust cutouts also serve to drive home the apple pie theme. The leaves provide just the right amount of buttery, flakiness to the cake. There is no mistaking that this is cake is based on classic American apple pie.
Make the cutouts: Preheat the oven to 425˚ F. Line a baking sheet with parchment paper. Stir together the granulated sugar and cinnamon. Unroll the pie dough and sprinkle the cinnamon sugar on top, pressing to adhere. Cut out about 20 leaf shapes using small cookie cutters. Arrange on the baking sheet and bake until golden, 8 to 10 minutes. Transfer to a rack and let cool.
Make the cake: Reduce the oven temperature to 350˚ F; butter a 9-by-13-inch baking dish. Whisk the flour, cinnamon, baking powder, salt, nutmeg, allspice and baking soda in a medium bowl. Beat the butter and vegetable oil in a large bowl with a mixer on medium-high speed until combined. Beat in both sugars until light and fluffy, about 4 minutes. Beat in the eggs, one at a time, then the vanilla. Reduce the mixer speed to low and beat in the flour mixture in three batches, alternating with the buttermilk in two batches. Increase the speed to medium high and beat until combined. Fold in the diced apples.
Transfer the batter to the baking dish and spread in an even layer. Bake until golden, slightly risen and a toothpick inserted into the center comes out clean, 35 to 45 minutes. Transfer to a rack and let cool completely in the pan.
Make the frosting: Set a heatproof bowl over a saucepan with 2 inches of barely simmering water. Add the brown sugar, egg whites and cinnamon to the bowl; stir with a rubber spatula until the sugar melts, about 8 minutes. (Pinch the mixture; it should feel smooth.) Remove the bowl from the pan and beat with a mixer on low speed until frothy. As the mixture begins to lighten in color, increase the speed to medium high and whip until stiff glossy peaks form. Beat in the butter 2 tablespoons at a time, making sure it is incorporated before adding more. (If the frosting separates, reduce the mixer to medium low and beat until it comes back together. If the frosting is soupy, refrigerate for 15 to 20 minutes, then continue beating.)
Spread the frosting on the cake. Decorate with the leaf cutouts.