Prepare the Baking Dish: Line an 8x8-inch baking dish with foil, pressing it firmly into the corners and leaving an overhang on the sides to make removal easier.
Melt the Chocolate: Place the white chocolate chips in a large mixing bowl and set aside.
Heat the Milk: In a microwave-safe bowl, warm the sweetened condensed milk for 90 seconds in the microwave.
Combine Milk and Chocolate: Carefully pour the heated condensed milk over the white chocolate chips. Let it sit for 1 minute to allow the chocolate to soften, then stir until the mixture is smooth and fully combined.
Add Flavoring: Stir in the rum extract, melted butter, and salt, mixing thoroughly. Taste and add more rum extract if a stronger flavor is desired.
Set the Fudge: Pour the fudge mixture into the prepared baking dish, smoothing the top with a rubber or offset spatula to create an even layer. Gently tap the dish on the table a few times to remove any air bubbles.
Garnish: Lightly dust the top of the fudge with ground cinnamon for added flavor.
Chill and Serve: Refrigerate the fudge for 2-4 hours, or until firm. Once set, lift the fudge out of the dish using the foil overhang and cut it into 36 pieces.