Preheat your oven to 350°F. Grease a 9×13-inch baking dish to prevent sticking.
Unroll one can of crescent roll dough and spread it evenly across the bottom of the baking dish. Press the seams together to form a uniform layer.
In a large bowl, beat the softened cream cheese with 1 cup of granulated sugar and the vanilla extract until the mixture is smooth and well combined.
Evenly spread the cream cheese mixture over the crescent roll dough layer in the baking dish.
Unroll the second can of crescent roll dough and place it carefully over the cream cheese layer. Press the seams together to create a smooth top layer.
Brush the melted butter evenly over the top layer of crescent roll dough. Mix the ground cinnamon and the remaining 2 tablespoons of granulated sugar in a small bowl. Sprinkle this mixture generously over the buttered dough.
Place the baking dish in the preheated oven and bake for 30 minutes, or until the top is crisp and golden brown.
Let the casserole cool for at least 20 minutes before slicing it into squares and serving.