Line (1) 8x8-inch pan with foil or parchment paper. Set aside.
In a large microwave-safe bowl, add the peanut butter, butter, and salt. Microwave on HIGH in 30-second increments, stirring after each, until the mixture is smooth and well combined. This will take anywhere from 90 seconds to 2 ½ minutes, depending on your microwave.
1 ¼ cups creamy peanut butter, 1 cup unsalted butter, ½ teaspoon fine sea salt
Stir in the vanilla extract, then add the powdered sugar to the peanut butter mixture 1 cup at a time, beating with an electric mixer on low speed after each addition until combined. Once all of the powdered sugar has been added, increase the speed to high and beat until the mixture is well combined and no lumps of powdered sugar remain.
1 teaspoon pure vanilla extract, 3 cups powdered sugar
Transfer the fudge mixture to the prepared pan. Press evenly into the prepared pan, smoothing the top with a spatula.
Chill in the refrigerator for about 2 hours, or until firm. Use the overhanging parchment or foil to lift the fudge from the pan; cut into small squares.
Notes
Store in an airtight container in the refrigerator for up to 2 weeks.
You can stir the powdered sugar in by hand if you don't have an electric mixer. I recommend sifting the powdered sugar first to get rid of any lumps before stirring it in by hand.