Line a 9-by-13-inch pan with foil. Bring the marshmallows, sugar, cream, butter and salt to a simmer in a medium saucepan over medium heat, stirring constantly. Continue to stir until the marshmallows melt and the sugar dissolves. Remove the saucepan from the heat, add the white chocolate chips and vanilla, and stir until the chips are completely melted.
Pour the mixture into the prepared pan and scatter the candy canes over the top. Let cool to room temperature, then wrap and refrigerate until chilled and firm, about 2 hours. Using the foil, lift the fudge from the pan and put on a cutting board. Cut the fudge into 1-inch squares.
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