Line your 9x9 inch baking dish with parchment paper, leaving some overhang on the sides for easy removal.
In a medium saucepan over medium heat, melt the butter until completely melted.
Stir in the evaporated milk and granulated sugar. Mix well until the sugar is dissolved.
Increase the heat slightly and bring the mixture to a boil, stirring constantly for about 5 minutes.
Remove from heat and stir in the chocolate chips and marshmallow cream until melted and smooth.
Stir in the vanilla extract until fully incorporated.
Pour the fudge mixture into the prepared baking dish, smoothing the top with a spatula.
Allow the fudge to cool at room temperature until fully set, or refrigerate to speed up the process.
Once set, lift the fudge out using the parchment paper and cut into squares.