Lightly oil or spray a 9×13 pan with vegetable spray.
In a 3-quart saucepan over medium heat, mix the sugar, butter and evaporated milk, stirring constantly until the mixture comes to a full rolling boil.
Clip the candy thermometer to the side of th pan and continue cooking for exactly 4 minutes or until the temperature reaches exactly 234 degrees F, stirring constantly. Remove from heat.
Stir in the chocolate and marshmallow creme and stir until completely melted. Add the vanilla and stir again.
Pour the fudge into the prepared 9×13 pan, spreading evenly. Sprinkle the chopped candy canes on top and let cool completely before cutting.
Using a 1 inch round cookie cutter, cut out fudge and place in mini baking cups to serve.