Mix the dry ingredients. In a mixing bowl, whisk together the flour, whole-wheat pastry flour, and salt.
Cut in the butter. Using a pastry cutter or a fork, cut in the butter and cream cheese; cut until the mixture is crumbly.
Add the wet ingredients. Stir in the oil and stir until the mixture is completely moistened. Add water and toss with a fork to combine.
Knead and chill the dough. Lightly flour your work area and knead the dough for 30 seconds. Shape the dough into a ball, press it into a disk, and wrap it in plastic wrap. Refrigerate for 30 minutes.
Make the Apple Filling
Combine the apples and spices. Place the apple slices in a mixing bowl and toss them with lemon juice. Add light brown sugar, cinnamon, and nutmeg; toss to combine. Sprinkle with flour and toss to combine; set aside.
Shape the crust. Remove the prepared dough from the fridge. Lightly grease a 9-inch pie dish with baking spray and set aside. On a lightly floured surface, roll out the dough into a 14-inch circle. Transfer the dough to the prepared pie dish and press it firmly into the bottom and up the sides of the dish.
Dock the crust. Prick the dough in several places with a fork. Place back in the fridge for 15 minutes.
Make the Cake Batter
Mix the dry ingredients. In a small bowl, whisk together the flour and baking powder until combined, then set aside.
Mix the wet ingredients. In your mixer's bowl, combine the eggs, sugar, and vanilla; beat for 1 minute or until pale yellow and fluffy.
Combine. Add the flour mixture to the egg mixture; set the mixer to low and continue mixing until combined, about 15 seconds.
Assemble. Preheat the oven to 425ºF. Remove the prepared crust from the fridge. Spoon the previously prepared apple mixture into the crust. Pour the cake batter over the apples.
Bake! Bake at 425ºF for 10 minutes. Then reduce the heat to 350°F and continue baking for 35 to 40 minutes, or until the top is lightly browned and set. If the top browns too quickly, tent loosely with foil for the last 10 to 15 minutes.
Cool and serve. Remove from the oven and let the apple pie cake cool for at least 20 minutes before cutting and serving.