In a medium saucepan, combine melted butter, granulated sugar, and sweetened condensed milk. Cook over medium heat, stirring constantly until the mixture thickens, about 5 minutes.
Remove from heat and stir in peanut butter, vanilla extract, and salt until smooth and fully combined.
Pour the mixture into a greased 8x8 inch pan and smooth the top.
Refrigerate for at least 2 hours or until set. Cut into squares and serve.
Notes
Store leftover fudge in an airtight container in the refrigerator for up to one week.