Line a 13×9-inch baking pan or casserole dish with wax paper and lightly spritz with cooking spray.
Place sweetened condensed milk, egg yolks, vanilla, rum extract, cinnamon, nutmeg, and salt in a medium bowl and whisk to combine.
Pour eggnog base into a medium saucepan, add white chocolate chips, stir to combine, and warm over low heat. Alternatively, you can use a double boiler.
Melt chips and slowly cook the fudge mixture, stirring frequently, until smooth and combined, about 10 minutes.
Remove from the heat and pour into the prepared baking dish.
Spread the fudge mixture evenly along the bottom of the pan and set aside to cool at room temperature.
Once cooled, cover and place in the refrigerator until firm, about 3 hours.
Cut fudge into squares before serving.