Preheat Oven: Set your oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish.
Prepare Cinnamon-Sugar Mixture: In a small bowl, combine sugar and cinnamon. Set aside.
First Layer: Roll out one can of crescent dough and press it into the bottom of the baking dish. Sprinkle generously with the cinnamon-sugar mixture.
Cheesecake Filling: Beat cream cheese, sugar, vanilla, and egg in a mixing bowl until smooth. Spread this mixture evenly over the dough.
Top Layer: Roll out the second can of crescent dough and place it over the cheesecake layer. Brush the top with melted butter and sprinkle with the remaining cinnamon-sugar mixture.
Bake: Bake for 30 minutes or until the top is golden brown and puffed.
Let the dish rest for a minimum of 15 minutes to cool before proceeding to slice it. Enjoy warm or chilled.