Line an 8x8-inch baking pan with parchment paper, leaving some overhang for easy lifting later. In a medium saucepan over medium heat, melt the butter and peanut butter together, stirring often until the mixture is smooth and starts to bubble gently around the edges. Remove from heat and stir in the vanilla and salt. Quickly add the marshmallows and stir until they melt completely into the mixture.

Using a wooden spoon or rubber spatula, stir in the powdered sugar one cup at a time until the mixture becomes thick and smooth. Work quickly, as it will begin to firm up. Transfer the fudge mixture to the prepared pan and press it evenly into the corners. Smooth the top with the back of the spatula and, if desired, sprinkle lightly with flaky sea salt for a sweet-and-salty finish.

Let the fudge cool at room temperature for 30 minutes, then cover and refrigerate for at least 2 hours, or until firm. Lift the fudge out using the parchment overhang and cut into squares with a sharp knife. Store in an airtight container at room temperature for up to 1 week, or in the fridge for up to 2 weeks.