Preheat oven to 350 F. Line an 8 x 8inch baking pan with parchment paper. Set aside.
Peel, core & grate apples. Sift flour, cornstarch, baking powder, cinnamon, allspice, cardamom & salt together in a medium bowl & set aside.
Using a mixer, cream butter & sugar until light. Scrape the bowl & add the whole egg, mixing on medium-high for about a minute. Scrape the bowl again & add the egg white & vanilla; mix for another 2 minutes.
Alternately fold in flour mixture & buttermilk, then gently fold in grated apples.
Pour/spread batter into prepared baking pan. Bake for about 30-40 minutes or until a cake tester comes out with just a few moist crumbs. Allow to cool in pan on a wire rack.
Baked Crisp Topping
Line a cookie sheet with parchment paper. Place all ingredients except butter in a bowl. Combine well then add softened butter. Mix until the mixture begins to form pea-sized clusters. Spread mixture evenly on the parchment lined cookie sheet, then bake at 350 F. for 5 minutes. Stir the topping around a bit, then bake for another 5 minutes until it begins to turn golden brown. Let crisp topping cool completely to room temperature. If crisp mixture is too chunky break it up with your fingers slightly.
Apple Topping
Place apples , lemon juice & water in a small saucepan. Cook over medium heat until softened, but not falling apart. Add brown sugar, cinnamon & salt. Cook for a minute to dissolve sugar. Remove & cool until cake is baked & ready to top.
Drizzle
Sift powdered sugar with salt. Set aside. Cream softened cream cheese & butter with a mixer for about 2 minutes. Add vanilla & mix to combine. Add powdered sugar & slowly incorporate into wet mixture. Add milk & beat to create a drizzle consistency.
Assembly
When cake is cool, carefully & evenly spread apple topping over top of cake. Using a small piping bag, drizzle icing over apples (using a spatula, lightly spread a bit of drizzle on sides). Next, top cake with baked crisp topping. Slice & serve.
Recipe Notes
To make your own buttermilk, place 2 tsp of white vinegar or lemon juice in your measuring cup & add milk to equal 2/3 cup, stir & let stand until room temperature.
If you prefer cupcakes over the snack cake, no problem. Same idea just a different shape. Your choice!