Preheat your oven to 350°F and lightly grease a 9×13-inch baking dish.
In a large mixing bowl, combine the cream cheese and 1 cup of sugar, then beat with an electric mixer until light and fluffy. Be sure to scrape down the sides of the bowl during mixing to ensure the cream cheese is fully incorporated and free of large chunks.
Add the vanilla extract to the cream cheese mixture and mix well.
Lightly flour a flat work surface, then open one can of crescent roll dough and lay it flat. Use a rolling pin to roll the dough into a 9×13-inch rectangle. Press the dough into the bottom of the greased baking dish.
Spread the cream cheese mixture evenly over the crescent roll dough in the pan using a small offset spatula or the back of a spoon.
Open the second can of crescent roll dough, roll it into a 9×13-inch rectangle just like the first, and place it on top of the cream cheese layer, covering it completely.
In a small bowl, combine the butter, remaining ¾ cup of sugar, and cinnamon. Dot this butter mixture on top of the crescent roll dough in the pan, distributing it evenly across the entire surface.
Bake the cheesecake for about 30 minutes, or until the top is golden brown.
Allow the cheesecake to cool before slicing and serving.