Prepare an 8x8 inch baking dish by lining it with parchment paper, leaving an overhang.
In a large bowl, combine marshmallow creme and white chocolate chips. Set aside.
In a medium saucepan over medium heat, combine unsalted butter, granulated sugar, and heavy whipping cream. Stir constantly until it comes to a gentle boil and bubbles for about 5 minutes.
Remove from heat and whisk in peppermint extract until smooth.
Pour the hot mixture over the marshmallow creme and white chocolate chips, stirring until fully combined and smooth.
Transfer the mixture into the prepared baking dish, spreading it evenly.
While the fudge is still warm, sprinkle crushed candy canes on top and gently press them in.
Chill the fudge in the refrigerator for at least 2 hours until firm.
Remove from the baking dish using the parchment paper overhang, and cut into squares.
Store in an airtight container in the refrigerator.
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Notes
Fudge can be stored in the refrigerator for up to two weeks, or frozen for longer storage.