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Preheat oven to 350°F with a rack in the middle of the oven. Grease a 9×13 baking pan and sprinkle 1-2 tablespoons cinnamon sugar in the bottom.
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Open one tube of crescent rolls. Unroll the dough and press the seams together to form one rectangular piece. Place into the bottom of the prepared 9×13 baking pan, it should cover the whole bottom of the pan.
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Combine cream cheese, sugar, egg, and vanilla, beating until smooth and well combined. Pour the cream cheese mixture over the crust and spread into an even layer.
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Using the second tube of crescent roll dough, unroll and press the seams together (just like you did with the first one) and place it over the cream cheese layer. It should cover the cream cheese completely.
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Pour melted butter over the top and spread it into an even layer (I use the back of a spoon). Sprinkle with remaining cinnamon sugar.
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Bake for 26-30 minutes, until the crescent dough has puffed and is golden brown. Place on a wire rack to cool completely, then transfer to the fridge until chilled. Once chilled, cut and serve.