In a large bowl, add the cream cheese, cinnamon, vanilla, and powdered sugar. Beat on the lowest setting with a hand mixer until creamy.
Fold in the whipped topping with a silicone spoon—don’t stir. Gently fold in the cinnamon roll pieces.
In a small bowl, microwave the cinnamon sugar butter for 15 seconds. Stir in the powdered sugar until thick enough to drizzle like icing. Add more powdered sugar if needed.
Put the cinnamon sugar mixture in a small ziplock bag. Cut off a small corner and drizzle over the dip in circles, starting from the center and getting bigger, just like a cinnamon roll swirl.
Sprinkle with extra cinnamon and top with more cinnamon roll pieces if desired. Serve with graham crackers, apple slices, or pretzels and enjoy!