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Place medium saucepan over medium heat and melt butter.
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Stir sugar, egg, vanilla extract and rum into the mix until it’s achieved a smooth, thick consistency and bring to a boil.
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Continue cooking, stirring constantly until the temperature reaches 234 degrees (soft ball stage for candy making).
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Turn off the heat, but leave on the hot burner. Slowly mix in the white chocolate chips until they are completely melted and smooth, then add in the marshmallow creme and continue stirring until fully blended.
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Lightly spray, butter, or line an 8x8 baking dish with wax paper and pour fudge mix inside. Refrigerate overnight or until mixture is set and not jiggly.
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Cut into squares before serving.