In a heavy-bottomed, good-quality saucepan (such as a 6-quart Le Creuset Dutch Oven), combine butter, sugar, and evaporated milk.
Turn the heat to high and start stirring. Continuously stir while the mixture comes to a rolling boil.
Continue stirring constantly for about 5 minutes or until it reaches a "soft ball" stage. If using a candy thermometer, it should read between 234 – 240 degrees. If you don't have a candy thermometer, perform a test: after 5 minutes, drop a small dollop of the sugar mixture into a glass of cold water. If it forms a soft ball "clump," the sugar mixture is hot enough. If the ball doesn't form, cook for another minute or so.
Remove the pan from the heat; stir in the chocolate chips and marshmallow creme. After a few stirs, add the vanilla. Mix until well blended, then add nuts and stir to combine.
Pour the mixture into a buttered 9 x 13-inch pan.
Let the fudge completely cool at room temperature before cutting it into squares.