Prepare an 8-inch baking dish by buttering it thoroughly, or line it with buttered parchment paper for easy removal, and set it aside.
In a medium saucepan, combine the unsalted butter and creamy peanut butter over medium heat. Stir the mixture gently until it reaches a gentle boil, then promptly remove it from the heat.
Add a pinch of salt and the vanilla extract to the hot mixture, stirring until fully incorporated. Gradually mix in the sifted powdered sugar, ensuring the mixture becomes smooth and free of lumps.
Pour the fudge mixture into the prepared dish, smoothing the surface with a spatula. Press a sheet of plastic wrap directly onto the surface of the fudge to prevent a skin from forming, and place it in the refrigerator to set for at least 1 hour.
Once firm, remove the fudge from the dish and cut it into squares. Store the fudge in an airtight container at cool room temperature for up to 1 week, or refrigerate for up to 1 month for longer shelf life. Enjoy!