Preheat the oven to 350 degrees F. Unroll one can of crescent rolls onto the bottom of a greased 9x13-inch baking dish, pressing the seams together.
Add the cream cheese, 1 cup of sugar, and cornstarch to a mixing bowl and beat until creamy. Then, add the egg and vanilla extract and beat until combined. Pour the cream cheese batter on top of the crescent roll dough and smooth with a spatula.
Unroll the second can of crescent rolls onto a cutting board and roll out to be a little longer and wider than the first layer to completely cover the cream cheese batter.
Melt the butter and pour over the top layer of dough.
Mix the cinnamon and ¼ cup of sugar together in a bowl and sprinkle on top of the melted butter. Bake for 35 minutes, then cool and chill in the refrigerator for 3 hours before cutting into squares.