Heat to 350°F (175°C) and grease an 8×8-inch baking dish to prevent sticking.
Prepare the crust: Press the cinnamon roll dough into the dish, pinching seams together. Brush with melted butter.
Make the cheesecake filling: Beat cream cheese, sugar, egg, and vanilla until smooth. Spread evenly over the crust.
Add the cinnamon swirl: Mix melted butter, brown sugar, and cinnamon. Drizzle over the cheesecake layer and swirl with a knife.
Bake for 25-30 minutes until the center is set and edges are golden.
Cool and finish: Let cool for an hour, then refrigerate for 1-2 hours. Drizzle with reserved icing before serving.