Prepare the baking dish by greasing it lightly or lining it with parchment paper for easy removal.
In a medium mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Mix until well combined.
Press the crust mixture firmly into the bottom of the prepared baking dish to create an even layer. Set aside.
In a large mixing bowl, beat the softened cream cheese using an electric mixer until smooth.
Add the creamy peanut butter, powdered sugar, and vanilla extract to the cream cheese. Beat until the mixture is well combined and creamy.
Gently fold in the whipped topping until fully incorporated.
Spread the cheesecake filling evenly over the crust.
In a microwave-safe bowl, combine the semi-sweet chocolate chips and butter. Microwave in 20-second intervals, stirring in between, until the chocolate is fully melted and smooth.
Pour the chocolate mixture over the cheesecake layer and spread it evenly using a spatula.
Refrigerate the bars for at least 4 hours or until set.
Once set, lift the bars out of the dish using the parchment paper (if used) and cut them into squares or rectangles.