Line an 8x8-inch or 9x9-inch baking pan with parchment paper or foil, leaving an overhang on two sides for easy lifting. Lightly grease the parchment with a small amount of butter or nonstick spray.

In a large mixing bowl, add the 3 cups powdered sugar and sift it, or whisk well to break up any lumps. Set the bowl next to your stove so it’s ready for the hot mixture.

In a medium (at least 3-quart) saucepan, combine the butter, granulated sugar, light brown sugar, and milk. Set over medium heat and stir gently as the butter melts and the sugar dissolves, scraping the bottom of the pan so nothing scorches.

Once the mixture is melted and smooth, bring it to a gentle boil over medium heat, stirring often. When it reaches a bubbling boil across the surface, boil for 3 minutes, stirring constantly, until the mixture looks silky and slightly thickened.

Turn off the heat and immediately stir in the peanut butter, vanilla extract, and salt. Continue stirring until the peanut butter is fully melted and the mixture is very smooth and glossy.

Carefully pour the hot peanut butter mixture into the bowl with the powdered sugar. Using a sturdy spatula or a hand mixer on low speed, mix until the powdered sugar is fully incorporated and the mixture is uniform and creamy, with no dry streaks.

Scrape the fudge mixture into the prepared pan and spread it out as evenly as possible. Use an offset spatula or the back of a spoon to smooth the top. If desired, tap the pan firmly on the counter a few times to help it settle.

Let the pan cool at room temperature for 10–15 minutes, then transfer to the refrigerator. Chill for 45–60 minutes, or until the fudge is firm enough to cut cleanly.

Use the parchment overhang to lift the fudge from the pan onto a cutting board. With a sharp knife, cut into 1-inch squares or desired size. For the cleanest cuts, wipe the knife with a warm, damp cloth between slices.