Preheat oven to 350°F. Grease a 12-cup bundt pan with non-stick cooking spray. Set aside.
In a small bowl, combine the brown sugar, granulated sugar, and cinnamon. Set aside.
Separate each biscuit and cut into quarters. Roll each biscuit piece into the cinnamon sugar mixture. Place about half of the biscuit pieces in the prepared bundt pan.
Spoon about half of apple pie filling over biscuits. Top with remaining biscuit pieces, followed by rest of apple pie filling. Set aside.
To make the caramel sauce, add brown sugar and melted butter to a small bowl. Stir thoroughly to combine. Pour sauce over biscuits.
Bake for 35-40 minutes, or until biscuits are golden and slightly set in the center. If biscuits brown too quickly, loosely cover the top of pan with foil. **Oven times vary, so your oven may need more time.**
Remove from oven and let rest for 5 minutes. Then, take a plate or platter and invert pan onto it. Let sit for 5 minutes so that the sauce soaks into bread.
To make the vanilla glaze, add powdered sugar, heavy cream, and vanilla extract to a small bowl. Stir to combine. Drizzle over warm bread. Serve immediately.