Prepare Cinnamon Sugar: In a small bowl, mix 1 tablespoon cinnamon with 1/2 cup sugar until well combined. Set aside.
Preheat and Prep Pan: Preheat oven to 350°F (175°C) and position rack in middle. Grease a 9×13-inch baking pan thoroughly and sprinkle 1-2 tablespoons of cinnamon sugar mixture evenly on the bottom.
Create Base Layer: Open one tube of crescent roll dough. Unroll carefully and press seams together to form a single rectangular sheet. Place into prepared pan, covering the bottom completely.
Make Cheesecake Filling: Beat softened cream cheese with electric mixer for 1 minute until smooth. Add 3/4 cup sugar and beat 1 minute until fluffy. Add egg and vanilla, beating on low just until incorporated. Pour over base layer and spread evenly.
Top Layer and Butter Coating: Open second tube of crescent dough, seal seams, and gently place over cheesecake filling. Pour melted butter over top and spread evenly with pastry brush.
Add Cinnamon Sugar Topping: Sprinkle remaining cinnamon sugar generously over buttered top layer.
Bake: Bake 26-30 minutes until crescent dough is puffed and golden brown. Remove from oven and cool on wire rack to room temperature (about 1 hour).
Chill and Serve: Cover cooled bars tightly with plastic wrap and refrigerate at least 3 hours or overnight. Slice into 16 bars before serving. Serve slightly chilled with optional toppings if desired.