Preheat oven to 350°F (175°C). Grease a 9-inch springform pan, line the bottom with parchment paper, and add a parchment collar. Press the cinnamon rolls evenly into the bottom, pinching gaps shut. Bake for 18 minutes, then remove and set aside. Reduce oven temperature to 300°F (150°C).

In a medium bowl, combine brown sugar, cinnamon, and flour. Stir in melted butter until a thick, crumbly mixture forms.

In a large mixing bowl, beat cream cheese, sugar, and flour on low speed until smooth. Add sour cream, vanilla, and cinnamon, mixing until just combined. Add eggs one at a time, mixing gently after each addition. Do not overbeat.

Wrap the springform pan securely in heavy-duty foil, or prepare a water bath. Sprinkle one-quarter of the cinnamon swirl mixture over the baked crust, followed by one-third of the cheesecake batter. Repeat layering two more times, finishing with the cinnamon swirl on top. Place the pan in a water bath and bake for 1 hour 20–30 minutes, until the edges are set and the center has a slight jiggle.

Turn off the oven and leave the cheesecake inside for 30 minutes with the door closed. Then crack the oven door and allow it to cool for an additional 30 minutes. Remove from the oven, cool to room temperature, and refrigerate for at least 6 hours or overnight.

Beat cream cheese and butter until smooth. Add vanilla extract and powdered sugar, mixing until combined. Add heavy cream one tablespoon at a time until a spreadable consistency is achieved. Pipe in a spiral pattern over the chilled cheesecake to resemble a cinnamon roll. Slice and serve.