Preheat oven to 350°F (175°C). Grease a 9×13-inch baking pan and line with parchment paper, leaving overhang for easy removal.
Make the bottom crust. Unroll one can of crescent dough and press it into the bottom of the prepared pan, sealing the seams. Brush with half the melted butter.
Make the filling. Beat cream cheese, sugar, and vanilla until smooth and creamy. Add the egg and beat just until combined — don't overmix.
Assemble. Spread cheesecake filling evenly over the bottom crust. Unroll the second can of crescent dough and place on top of the filling, gently stretching to cover and sealing the seams. Brush with remaining melted butter.
Add cinnamon sugar. Mix sugar and cinnamon together. Sprinkle evenly over the top crust. Some will soak into the butter and some will stay on top for that classic churro crunch.
Bake for 30–35 minutes until the top is golden brown and the center is just set with a slight jiggle. It will firm up as it cools.
Cool and chill. Let cool completely at room temperature, then refrigerate at least 2 hours (preferably overnight) for cleanest slicing.
Serve. Lift out using parchment overhang. Cut into 12 squares. Dust with extra cinnamon sugar if desired.
