Preheat oven to 350 degrees. Line a 9X13-inch pan with aluminum foil or parchment paper, letting excess extend over sides.
Make crust. In a large bowl, using an electric mixer, beat butter and brown sugar until smooth and fluffy. Add flour and salt and beat until combined. Press into bottom of prepared pan.
Bake for 20 minutes. Let cool completely.
In a large bowl use an electric mixer to beat cream cheese until smooth. Beat in eggs and 3/4 cup granulated sugar. Beat in vanilla extract. Spread mixture evenly on top of cooled crust.
Mix together apples, 1/3 cup sugar, and 1 teaspoon cinnamon. Sprinkle apple mixture over cheesecake mixture.
In a medium bowl, combine 1 cup flour, 3/4 cup brown sugar, oats, salt, cinnamon, and pecans. Stir in butter until mixture resembles coarse crumbs. Sprinkle mixture over apples.
Bake 50 minutes. Let cool until room temperature and then refrigerate until chilled.
When serving, drizzle with caramel topping.