Preheat the oven to 350°F. Lightly grease a 9×13-inch baking dish.
Unroll 1 can (8 ounces) of crescent roll dough and press it evenly into the bottom of the prepared baking dish. Pinch the seams together to create one solid layer.
In a medium mixing bowl, beat together 4 packages (8 ounces each) of softened cream cheese, 2 teaspoons vanilla extract, 2 large eggs, 1/2 teaspoon ground cinnamon, and 1 1/2 cups sugar until smooth and fluffy, about 2 minutes.
Spread the cream cheese mixture evenly over the crescent roll dough.
Unroll the second can (8 ounces) of crescent roll dough. Carefully place it over the cream cheese layer, gently stretching it as needed to cover the entire surface. Pinch the seams together.
Pour 4 tablespoons melted unsalted butter evenly over the top of the crescent roll dough and spread it gently to coat.
In a small bowl, whisk together the remaining 1/4 cup sugar and remaining 2 teaspoons ground cinnamon.
Sprinkle the cinnamon-sugar mixture evenly over the buttered dough.
Bake for about 50 minutes, or until the crescent dough is puffed and cooked through and the center is set.
Remove from the oven and let cool for 30 minutes before cutting.
Cut into 9 pieces and serve.