Step 1: Preheat your oven to 325°F (160°C). Lightly grease a 9-inch springform pan with cooking spray or butter.
Step 2: Remove the cinnamon rolls from the package (reserve the icing for later). Flatten each cinnamon roll slightly and arrange them in a single layer on the bottom of the prepared springform pan. Press them together firmly with your fingers to create a solid, even crust.
Step 3: In a large bowl, using an electric hand mixer, beat the softened cream cheese and granulated sugar together until smooth and creamy, about 2-3 minutes.
Step 4: Add the sour cream and vanilla extract to the cream cheese mixture and beat until just combined.
Step 5: Add the eggs one at a time, beating on low speed after each addition just until incorporated. Do not overmix after adding the eggs, as this can lead to cracks.
Step 6: In a small separate bowl, combine the melted butter, light brown sugar, and ground cinnamon for the swirl. Whisk until well combined.
Step 7: Pour the cheesecake filling over the cinnamon roll crust in the springform pan, spreading it gently and evenly.
Step 8: Dollop spoonfuls of the cinnamon-butter mixture over the top of the cheesecake filling. Use a knife or skewer to gently swirl the cinnamon mixture into the cheesecake, creating a beautiful marbled effect. Be careful not to swirl too much or scrape the bottom crust.
Step 9: Bake for 55-60 minutes, or until the edges are set and lightly golden, but the center still has a slight jiggle when gently shaken.
Step 10: Turn off the oven, crack the door open slightly, and let the cheesecake cool in the oven for 1 hour. This helps prevent cracks.
Step 11: Remove from the oven and let it cool completely on a wire rack at room temperature. Once cooled, cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, for best results.
Step 12: Before serving, gently remove the cheesecake from the springform pan. Warm the reserved cinnamon roll icing slightly (you can microwave it for a few seconds) and drizzle generously over the chilled cheesecake. Slice and enjoy!