Prepare the oven and baking dish.
Preheat your oven to 350°F (175°C). Have a 9×13-inch baking dish ready for assembling the cheesecake.
Make the cheesecake filling.
Add the softened cream cheese, 1 ½ cups of sugar, and vanilla extract to a large mixing bowl. Beat until the mixture becomes creamy, smooth, and evenly combined.
Prepare the crescent dough.
Open both cans of crescent roll dough. Gently roll or press each portion into approximately a 9×13-inch rectangle, sealing any perforated seams as needed.
Create the bottom layer.
Place one rectangle of crescent dough across the bottom of the baking dish. Gently press it into an even layer.
Add the cream cheese mixture.
Spoon the cheesecake filling over the dough and spread it evenly from edge to edge with a spatula.
Add the upper pastry layer.
Carefully position the second sheet of crescent dough over the cream cheese filling. Gently adjust the dough so it covers as much of the filling as possible.
Add the butter.
Slowly pour or drizzle the melted butter across the surface of the crescent dough, spreading it around if necessary so the top is evenly coated.
Make the cinnamon-sugar topping.
Combine the remaining ½ cup of granulated sugar with the cinnamon in a small bowl. Sprinkle the mixture generously over the buttered dough, then scatter the sliced almonds evenly across the top.
Bake.
Place the baking dish in the preheated oven and bake for approximately 45 minutes, or until the top layer of crescent dough is puffed and deeply golden.
Cool and slice.
Remove the cheesecake from the oven and allow it to cool completely inside the pan. For the cleanest slices, refrigerate it after cooling before cutting it into 12 squares.