Preheat oven to 350°F (175°C) and spray a 9x13-inch baking pan with cooking spray.
In a food processor, combine 2 cups flour, ½ cup brown sugar, and ¾ cup cold butter. Pulse until crumbly, press half into the prepared pan, and bake for 15 minutes.
Beat cream cheese until smooth. Add sugar, vanilla, and eggs one at a time until well combined.
In a bowl, toss diced apples with cinnamon, nutmeg, and 2 tablespoons sugar.
In the food processor, combine ¾ cup flour, ¾ cup brown sugar, oats, and ⅓ cup cold butter until crumbly.
Spread cheesecake filling over baked crust. Layer apple mixture evenly on top, then sprinkle crumb topping.
Bake uncovered for 25–35 minutes or until golden brown on top. Cool completely before slicing.
Optional: drizzle with caramel sauce before serving.
