Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish or line it with parchment paper for easier removal.
In a small bowl, stir together the granulated sugar and cinnamon until evenly combined. Set aside.
Unroll one sheet of crescent dough and gently press it into the bottom of the prepared baking dish. If using crescent rolls, pinch the seams together to create one smooth layer.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy. Add the sugar, egg, vanilla extract, and salt. Beat for 1–2 minutes until the filling is silky and well combined.
Spread the cheesecake filling evenly over the bottom pastry layer using an offset spatula or the back of a spoon.
Carefully place the second sheet of crescent dough over the filling, gently stretching it to cover the entire surface.
Brush the melted butter evenly over the top layer of dough.
Sprinkle the cinnamon sugar mixture evenly over the butter, covering the entire surface.
Bake for 28–32 minutes, or until the top is golden brown, puffed, and crisp around the edges. The center should appear set with only a slight wobble.
Remove the pan from the oven and cool at room temperature for about 30 minutes.
Refrigerate for at least 2 hours before slicing. Chilling allows the cheesecake layer to firm up and makes cutting clean bars much easier.
Slice into 16 squares and serve chilled or slightly cool.