Preheat oven to 350F and grease & flour three 6" cake pans. Line with parchment.
In a medium bowl, whisk together flour, pumpkin pie spice, baking powder, baking soda, and salt.
In a large bowl, whisk together sugars, oil, pumpkin, vanilla, and eggs.
Add dry to wet and mix until just combined.
Divide batter evenly between prepared pans and bake until a toothpick inserted into the center comes out mostly clean (approx. 30-35 mins).
Cool in pans on wire rack for 10mins, then turn out onto wire racks to cool completely.
Apple Pie Filling:
Toss chopped apples and lemon juice in a large bowl, set aside.
In a large saucepan, combine sugars, cornstarch, and spices. Pour in water and whisk.
Cook over medium heat until boiling. Cook for 2 minutes, stirring occasionally. Add apples, bring back to a boil. Simmer, stirring occasionally, until tender (10-15mins). Cool completely.*
Cream Cheese Frosting:
Beat butter and cream cheese until pale and fluffy (2 mins). Add powdered sugar one cup at a time. Add vanilla and beat until fluffy.
Place one layer of cake on a cake stand or serving plate. Top with about 1/2 cup of frosting and spread evenly.
Pipe a border of frosting around the outside to hold in the apple pie filling. Fill with about 1/2 cup apple pie filling, spread evenly.** Repeat with next layer. Place final layer on top and do a thin crumb coat on the cake. Chill for 20mins.
Frost the top and sides of the cake with remaining frosting in a rustic manner. Decorate with dried apple slices or cake crumbs if desired.
* You can make the apple pie filling in advance. Transfer to glass container, cool completely, refrigerate. Bring to room temp and give a good stir before using. Will keep for 2 weeks in the fridge.** If your frosting is really soft, you may want to chill each layer before stacking the next to firm the frosting up.