Preheat the Oven: Preheat the oven to 350°F and grease or line with parchment a 9×13-inch baking dish. This way, the bars will pull straight out of the pan when they are baked and cooled.
Prepare the Cinnamon Sugar Mixture: In the same small bowl, combine ½ cup white sugar with 2 tablespoons powdered cinnamon. Fold them into each other until the cinnamon coats every crystal of sugar. You need that mixture to impart that signature churro taste and mouthfeel into the sweet treat. Set it aside for later use.
Make the Cream Cheese Filling: With an electric mixer, either handheld or stationary, whip two 8-ounce packages of cream cheese (at room temperature) until the mixture becomes perfectly creamy. Gradually add ¾ cup sugar, followed by 1 large egg and 1 teaspoon vanilla extract. Mix thoroughly until the filling becomes smooth without any lumps. Use a spatula to periodically clean the bowl's edges, ensuring all ingredients are mixed thoroughly.
Prepare the Base Layer: Begin by taking a sheet of crescent dough from the first container. Place it on a clean countertop and carefully spread it out. Transfer the dough after flattening it onto your baking pan, then spread it uniformly across the base using your fingertips. When working with crescent rolls, make sure to seal any perforated lines to create one solid layer of dough.
Add the Filling: Cover the base layer entirely with an even spread of the cream cheese mix. Spread it evenly to the edges using a spatula to ensure every bar has a consistent layer of cheesecake filling.
Top with the Second Dough Sheet: Roll out the second crescent dough sheet. Carefully lay it over the cream cheese layer, pressing lightly to ensure it covers the filling completely. If seams are visible, pinch them together to seal.
Brush with Butter and Sprinkle the Topping: Take 2 tablespoons of unsalted butter, heat until liquified, and spread it thoroughly across the uppermost layer of dough. Immediately sprinkle the prepared cinnamon sugar mixture generously across the buttered surface. This step gives the bars their churro-inspired finish.
Bake to Perfection: Transfer the dish to the oven once it has reached the correct temperature. Let it cook for approximately 25-30 minutes. You'll know it's ready when you see a golden-brown color on top and notice the sides have risen and become puffy. For uniform cooking results, turn the pan around at the midpoint of baking time.
Cool and Chill: Take the bars out of the oven and let them sit at room temperature for about 30 minutes until they have cooled completely. Place in the refrigerator and let it cool for 2 hours minimum, though leaving it overnight will give you ideal consistency.
Slice and Serve: Once chilled, slice the dessert into 16 evenly-sized bars. Enjoy it plain, or enhance your dessert by adding a stream of caramel and a swirl of chocolate sauce, or top it with freshly made whipped cream.