Sift sugar through a fine-mesh strainer into a large bowl.

Heat butter and peanut butter in a saucepan over medium heat. Whisk to combine and cook until bubbles appear on the edges, 3 to 5 minutes. Stir in salt and vanilla extract. Pour over powdered sugar in the bowl. Mix together using a spatula until smooth.

Spread mixture into an 8x8-inch baking pan lined with plastic wrap. Wrap fully and refrigerate until firm enough to cut but not too hard, 1 to 3 hours.

Unwrap fudge and cut into small cubes. Let warm up on the counter before cutting if needed.