Line an 8x8 inch square baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a heavy-bottomed saucepan over low heat, combine the white chocolate chips, sweetened condensed milk, butter, and salt.
Stir the mixture constantly with a silicone spatula until the chocolate is completely melted and the texture is smooth.
Remove the saucepan from the heat and stir in the vanilla extract.
Transfer approximately 3/4 cup of the fudge base into a separate small bowl and vigorously stir in the cinnamon and brown sugar until fully integrated.
Pour the remaining white chocolate base into the prepared baking pan and spread into an even layer.
Drop spoonfuls of the cinnamon-sugar mixture onto the white base.
Using a butter knife or a skewer, swirl the cinnamon mixture through the base to create a marbled effect.
Cover the pan and refrigerate for at least 2 hours or until the fudge is completely set and firm.
Lift the fudge out of the pan using the parchment paper overhang and slice into 1-inch squares using a sharp, warm knife.