Line an 8-inch x 8-inch baking dish with foil, pressing it into all of the corners and allowing it to hang over the edges a bit. Set aside.
Place the white chocolate chips in a mixing bowl.
Pour the sweetened condensed milk into a microwave-safe bowl and heat in the microwave for 1 minute 30 seconds. Carefully remove the bowl and immediately pour the milk over the chocolate chips.
Allow the chocolate chip to melt for 1 minute before stirring. Stir until combined and smooth. (There should be no chocolate chip chunks hanging out.)
Pour in the rum and butter and add the salt. Carefully mix until completely combined. This will take a couple of minutes, don't rush it.
Pour the fudge mixture into the prepared dish. Use a rubber or offset spatula to smooth the fudge into an even layer. Tap the dish on the table a couple times to remove any bubbles.
Sprinkle a light dusting of cinnamon all over the top of the fudge.
Refrigerate for 2-4 hours, or until the fudge has set. Remove the fudge from the fridge and cut into 36 pieces.