Line a 13x9-inch baking pan with parchment paper (or lightly grease it). This will make it easy to remove the bars for cutting and serving.
For the bottom layer, in a large bowl, combine the softened butter, peanut butter, powdered sugar, graham cracker crumbs, vanilla, and salt. Stir with a wooden spoon or use a hand mixer until the mixture is well-blended and forms a smooth, thick dough-like consistency. Add additional powdered sugar if it appears too thin.
Transfer the peanut butter mixture into the prepared pan. Press it firmly and evenly into the bottom to form the crust layer.
For the top layer, In a microwave-safe bowl, combine chocolate chips and peanut butter. Microwave in 20–30 second intervals, stirring well after each, until the mixture is melted and smooth.
Pour the melted chocolate-peanut butter mixture over the base layer. Use a spatula to spread it in an even layer. Make sure the chocolate covers the peanut butter base completely.
Refrigerate the pan for at least 1 hour, or until the top chocolate layer is firm and set.
Once the chocolate is set, lift the slab of bars out of the pan using the parchment paper (if you used it) and place it on a cutting board. Use a sharp knife to cut into squares or bars of your desired size.