Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a small bowl, mix the sugar and cinnamon for the crust. Set aside.
Unroll one can of crescent roll dough and press it into the bottom of the prepared dish, sealing any seams. Sprinkle half of the cinnamon-sugar mixture evenly over the dough.
In a large bowl, beat the cream cheese, sugar, vanilla extract, and egg until smooth. Spread the cream cheese mixture evenly over the dough layer.
Unroll the second can of crescent roll dough and carefully place it on top of the filling, pressing to seal any seams.
Sprinkle the remaining cinnamon-sugar mixture over the top layer of dough.
Bake for 30 minutes, or until the top is golden and puffed.
Let the cheesecake cool completely at room temperature, then refrigerate for at least 2 hours to set.
Slice into squares or bars and serve. Enjoy your delightful Churro Cheesecake!