Preheat an oven to 350º F (175º C).
Beat the cream cheese with 1 1/2 cups of sugar, and the vanilla extract in a bowl until smooth.
Unroll the cans of crescent roll dough and use a rolling pin to shape the each piece into 9x13 inch rectangles. Press one piece into the bottom of a 9x13 inch baking dish.
Evenly spread the cream cheese mixture into the baking dish, then cover with the remaining piece of crescent dough.
Drizzle the melted butter evenly over the top of the cheesecake. Stir the remaining 1/2 cup of sugar together with the cinnamon in a small bowl, and sprinkle over the cheesecake.
Bake in the preheated oven until the crescent dough has puffed and turned golden brown about 45 minutes.
Cool completely in the pan before cutting into 12 squares.