Grease an 8-inch-square pan with butter. Line the bottom with parchment paper, then grease the paper.

In a medium saucepan, combine the butter and peanut butter. Cook over medium-low heat, stirring often, until melted and smooth, 3 to 4 minutes. Do not let the mixture come to a simmer. Off the heat, stir in the vanilla and salt.

Scrape the peanut butter mixture into a large bowl. Gradually add the confectioners’ sugar a few spoonfuls at a time, whisking until the sugar is fully incorporated after each addition. After all the sugar has been added, mix well with a rubber spatula until smooth.

Transfer the mixture to the prepared pan and smooth the top. Cover with plastic wrap, pressing the plastic to the surface of the fudge. Chill for at least 2 hours, until set. Use a knife to cut the fudge away from the pan, then lift the parchment paper to remove it. Cut into 1-inch squares. Store fudge, covered, in the refrigerator for up to 5 days or freeze for up to 2 months (see Tip).