Preheat oven to 350°F and coat a 9x13-inch baking dish with the softened butter. Unroll one can of crescent roll dough and lay it evenly along the bottom of the prepared dish, gently pressing the seams together without flattening the dough excessively. In a large bowl, combine softened cream cheese, sugar, and vanilla, then beat until creamy and smooth using a hand mixer. Distribute the cheesecake mixture in large spoonfuls across the bottom crust and spread to cover evenly. Carefully unroll the second can of crescent roll dough and place it over the cheesecake filling, ensuring it covers the surface without pressing into the filling. Melt the butter in the microwave and pour it over the top layer of dough, using a knife to spread it evenly. Mix cinnamon with the remaining sugar in a small bowl, then sprinkle uniformly over the buttered top. Bake for 25–30 minutes, or until the surface turns golden and the sugar forms a light crust. Allow bars to cool completely before slicing and serving. Store in the refrigerator to preserve the filling.