Line a 9 by 9-inch square baking pan with foil, or do the same with an 8 by 11-inch pan. Extend the foil slightly over the end of the pan, so that the fudge will be easy to lift out later if you need to store the fudge in another container.
Bring sugar, butter, and evaporated milk to a rolling boil in a large (mine is 2 and 3/4-quart-sized) saucepan on medium heat. Stir the mixture constantly. Keep stirring and boil for 4 minutes or until a candy thermometer reaches 234 degrees. Remove the pan from the heat.
Stir in the peanut butter and marshmallow creme and keep stirring until both are melted. Add vanilla and mix well.
Pour into prepared pan, spreading to cover the pan completely. Cool for a few hours before cutting into small squares. If you need to put the fudge in a different container for storage, lift the fudge out of the pan (using foil handles) before cutting.