Position your oven rack in the center and preheat the oven to 400ºF (200ºC). Lightly coat a 9x13-inch baking dish with nonstick cooking spray. Unfold the first sheet of puff pastry and place it flat in the prepared dish. Don’t trim the edges, as the dough tends to shrink slightly during baking. Press the pastry gently into the corners and up the sides, making sure it fits snugly. Prick the bottom of the pastry several times with a fork to prevent it from puffing up too much in the oven. Bake the crust for 15 minutes, or until lightly golden.
While the crust is baking, prepare the cheesecake filling. In a mixing bowl, beat the softened cream cheese with 1 cup of the granulated sugar until smooth and creamy, about 2 minutes. Add in the egg, sour cream, and vanilla extract, and blend just until incorporated—this should only take about 5 to 10 seconds to avoid overmixing. The mixture should be silky and uniform.
Remove the baked crust from the oven. If it has puffed slightly, allow it to rest for 5 minutes to settle. Spoon the cheesecake filling over the warm crust and spread it evenly using an offset spatula. Carefully lay the second sheet of puff pastry over the filling. Tuck in or gently crimp the edges to encase the cheesecake mixture.
In a small bowl, stir together the remaining ¼ cup sugar with the ground cinnamon. Using a pastry brush, apply half of the melted butter over the top layer of puff pastry. Generously sprinkle the cinnamon-sugar mixture over the entire surface, then drizzle the remaining melted butter across the top for a glistening, buttery finish. Don’t worry about being precise—the rustic finish adds charm.
Return the dish to the oven and bake for 20 to 25 minutes, or until the top layer of puff pastry is fully baked and golden. If the crust puffs up during baking, allow it to cool naturally so the steam escapes. You can also poke a small hole with a paring knife to release excess steam.
Let the bars cool at room temperature for at least 20 minutes. Then refrigerate the dish for several hours—or preferably overnight—until fully set. This ensures clean, sharp slices. When ready to serve, cut the bars using a clean, sharp knife, wiping the blade between each cut for crisp edges.