Preheat oven to 350°F. Grease a 9×13-inch baking pan and sprinkle 1–2 tablespoons of cinnamon sugar into the bottom of the pan.
In a small bowl, combine cinnamon and sugar. Set aside.
Open one tube of crescent roll dough. Unroll and press the seams together to form one rectangle. Place the dough into the prepared pan, covering the bottom completely.
In a mixing bowl, beat cream cheese, sugar, egg, and vanilla extract until smooth and creamy.
Pour the cheesecake mixture over the bottom crust and spread evenly.
Unroll the second crescent dough sheet, press seams together, and carefully place over the cheesecake layer.
Pour melted butter over the top layer and spread evenly using the back of a spoon or pastry brush.
Sprinkle the remaining cinnamon sugar generously over the top.
Bake the Churro Cheesecake Bars for 26–30 minutes, or until golden brown and puffed.
Cool completely on a wire rack, then refrigerate until chilled before slicing and serving.