Line an 8×8 inch square baking pan with parchment paper leaving an overhang to use as handles. Roughly chop the white chocolate bars and set aside.
In a heavy medium-sized saucepan over medium heat, combine the butter, sugar, eggnog, and salt. Bring it to a rolling boil, stirring constantly. Boil for 8 to 10 minutes, or until a candy thermometer reaches 234 degrees F (soft ball stage). Remove from the heat.
1/2 cup Unsalted butter, 2 cups Granulated sugar, 3/4 cup Eggnog, 1/4 tsp Kosher salt
Working quickly, stir in the white chocolate and grated nutmeg until all the chocolate is melted and smooth. With a wooden spoon beat in the marshmallow creme and rum extract until completely combined.
10 1/2 oz White chocolate, 1/2 tsp Freshly grated nutmeg, 7 oz Marshmallow creme, 1 tsp Rum extract
Pour the eggnog fudge into the prepared pan and sprinkle additional freshly grated nutmeg over the top for garnish. Let cool to room temperature and then refrigerate for 4 hours up to overnight.
Remove the fudge from the pan using the overhang of parchment paper. Cut the fudge in half one way and then the other to make four equal squares. Cut each small square into thirds one way and then the other, resulting in 9 equal pieces. You should have 36 equal pieces of fudge.