Prep your tools. Preheat your oven to 350˚F. Line a 9x13 glass baking dish with aluminum foil, leaving a generous overhang on either end so that you can lift the cheesecake out of the pan later. Spray with cooking spray and set aside.
Make the cinnamon sugar. In a small bowl, combine the ground cinnamon and sugar. Set aside.
Make the cookie crumb base. Place the cookies in your food processor and pulse until the cookies resemble breadcrumbs. Add the sugar and cinnamon, then pulse a few times to blend. Pour the melted butter over the crumbs, then pulse until the butter has been worked in. You should have a cookie crumb mixture that looks moist and sticks together when you press it with your fingers.
Add crumbs to the prepared baking dish. Remove the blade and scrape down the sides of your food processor with a spatula. Transfer the cookie crumbs to your prepared 9x13 baking dish. Spread them out to cover the bottom of the pan.
Form the crust. Using your spatula or the back of a metal spoon, firmly but gently press the crumbs down. Don't press so hard that you crumble the crust. You just want to press down enough for the crumbs to stick together. Go along the edges of the pan to make sure the edges are pressed too. Set aside.
Add some of the cinnamon sugar. Sprinkle 1½ tablespoons of the previously prepared cinnamon sugar mixture over the crust. Set aside.
Make the cheesecake filling. In the bowl of a stand mixer or a large bowl, combine the softened cream cheese, sugar, egg, and vanilla. Using the paddle attachment or a large whisk attachment if using a hand-held mixer, beat the ingredients until well combined. Scrape down the sides of the bowl with a clean spatula.
Add the filling to the baking dish. Spoon the cream cheese mixture over the cookie crust and spread it evenly with a spatula.
Make the top crust. Remove the crescent roll dough from the tube and spread it out on a clean surface. Press the seams together so that the dough forms one rectangular piece. Carefully transfer to your baking dish, placing the dough over the cheesecake filling. Arrange the dough so that it covers the filling completely.
Add butter and cinnamon sugar. Spread the melted and cooled butter over the dough with a pastry brush or a metal spoon. Sprinkle the remaining prepared cinnamon-sugar on top.
Bake. Place the cheesecake in the oven and bake for 25-30 minutes, until the crescent dough crust has puffed up and is golden.
Cool. Remove the cheesecake from the oven and let it cool to room temperature.
Chill. Cover the cheesecake with saran wrap and place it in the fridge to chill overnight.