For the cake, preheat oven to 350 degrees. Grease and flour two (9-by-2-inch) round cake pans; set aside. In a large bowl, whisk together whole wheat pastry flour, all-purpose flour, baking powder, baking soda, cinnamon and salt. Set aside. In a second large bowl, beat sugar and oil together with an electric mixer until well combined, about 30 seconds. Add applesauce, dulce de leche and vanilla, beat for 30 seconds, then add eggs one at a time, beating well after each addition. Add flour mixture in three parts, alternating with the buttermilk, and continuing to beat until well combined.
Pour batter into prepared cake pans and bake until golden brown and a toothpick inserted in the middle of each cake comes out clean, about 40 minutes. Set aside to let cool for 10 minutes, then gently loosen cakes and turn out onto a cooking rack; set aside to let cool completely.
For the frosting, put sugar, butter, cider, cinnamon and salt into a large bowl and beat with an electric mixer until light and fluffy, about 5 minutes. Arrange one cake on a large plate and spread about 2/3 cup of the frosting evenly over the top. Arrange second cake on top then frost top and sides of entire cake with remaining frosting. Decorate with dried apple slices, if you like, then set aside at room temperature or in the refrigerator for at least 1 hour to allow frosting to set before serving.