Prepare the graham cracker crust by blending graham crackers into fine crumbs, mixing with brown sugar and melted butter, and pressing into a 9-inch springform pan. Bake at 325ºF for 10 minutes and let cool.
Create the apple crumble topping by peeling, coring, and chopping apples. Mix flour, brown sugar, and cinnamon, then mix in butter until crumbly. Mix remaining crumbs with chopped apples and chill.
Make the cheesecake batter by beating cream cheese until smooth, adding sugars, sour cream, and applesauce, incorporating eggs one at a time, and mixing in vanilla extract, salt, and cinnamon powder.
Assemble the cheesecake with half of the batter, apple crumble mixture, remaining batter, and top with reserved crumble.
Bake in a water bath at 325ºF for 60-75 minutes until the edges are set. Cool with the oven door ajar.
After cooling, refrigerate for at least 6 hours or overnight. Store in an airtight container for up to 4 days.