Preheat your oven to 350°F and grease a 9×9-inch baking dish exceptionally well with butter or non-stick spray.

Unroll the refrigerated crescent roll dough onto a clean surface and split it into two equal, matching sections.

Lay the first section of dough into the bottom of the prepared baking pan. Use your fingers to aggressively pinch all the perforated triangle lines closed to create a solid sheet. Pro Tip: Creating a unified, gap-free dough base is crucial. If the seams aren't sealed tightly, the heavy moisture from the warm cheese filling will leak underneath the crust, gluing the pastry directly to the pan and making it impossible to slice cleanly.

In a medium bowl, combine the softened cream cheese, vanilla extract, ½ cup of sugar, and both the juice and freshly grated zest of the 2 lemons. Beat with a hand mixer on medium speed until the mixture is entirely smooth, airy, and free of lumps.

Pour the lemon cream cheese mixture directly over the bottom dough base, using a rubber spatula to smooth it into a perfectly level layer right up to the edges.

Gently hover the second section of dough directly over the filling, aligning the corners perfectly before dropping it into place. Pinch its interior seams shut just like the base layer. Bake uncovered for 25 to 30 minutes until the top pastry sheet puffs up and turns a deep, beautiful golden brown.

The moment you pull the pan from the hot oven, brush the melted butter evenly across the surface of the warm dough. Immediately scatter the final 1 tablespoon of sugar over the wet butter to create a sweet, glistening top crust.

Let the pan sit on a wire rack until it cools completely to room temperature. Once cool, transfer the pan directly to the refrigerator and chill for a minimum of 6 hours (or overnight). Crucial: When hot, the whipped cream cheese filling is completely fluid. Giving it a long, uninterrupted cold rest allows the dairy lipids to firmly lock back together, transforming the filling into a dense, velvety cheesecake texture that won't squish out when cut. Slice into even squares and serve chilled.