Butter an 8-inch non-stick baking dish (or line with buttered parchment paper) and set aside.
In a medium saucepan over medium heat, heat the butter and peanut butter until the mixture comes to a boil. Remove from the heat.
Add the salt and vanilla extract, then stir in the powdered sugar until smooth and no lumps remain.
Pour the fudge mixture into the prepared pan and smooth the top. Press a piece of plastic wrap directly on the fudge and refrigerate until set, at least 1 hour. Cut into squares and serve. Fudge can be stored at cool room temperature in an airtight container for up to 1 week, or in the refrigerator for up to 1 month.
Notes
You can make this in the microwave! Place the butter and peanut butter in a large microwavable bowl; cover with a paper towel and microwave on high for 2 minutes. Stir, microwave for 2 more minutes, then proceed with the rest of the recipe as written.
If you don't have an 8-inch square pan, you can use a 9-inch square pan, but the fudge will not be as high.
The fudge can be stored in an airtight container or in a freezer ziploc bag for up to 3 months.