Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal later.
In a large microwave-safe bowl, combine the peanut butter and butter. Microwave on high for 2 minutes, then stir until completely smooth and combined.
Add the vanilla extract and salt, stirring well to incorporate.
Gradually add the powdered sugar, one cup at a time, stirring well after each addition until the mixture is smooth and creamy.
Pour the fudge mixture into the prepared pan and spread evenly with a spatula. Smooth the top.
Refrigerate for at least 2 hours until firm, then lift out using the parchment paper and cut into 1-inch squares.
Store in an airtight container in the refrigerator for up to 2 weeks, or freeze for up to 3 months.