Preheat the oven to 350 degrees F. Line an 8x8 inch baking pan with parchment paper.
Heat a small skillet on medium high and add the eggnog. Simmer, stirring frequently, until the mixture is reduced. It will look thick, slightly yellow, and almost like a paste. Allow to cool to room temperature.
Beat the reduced eggnog with the cream cheese until completely combined. Beat in the egg, sugar, and nutmeg if using. Set aside.
On a double boiler, add the butter and chocolate together and melt.
Mix to combine. Remove the top pot of your double boiler from the heat and allow to cool slightly before beating in the sugar and eggs. Add in the vanilla, then the cocoa powder, flour, and salt.
Pour ¾ of the brownie mixture into the pan, then top with the eggnog cheesecake filling, making sure the cheesecake is spread evenly.
Dollop the remaining ¼ of the brownie mixture over the cheesecake mixture and then swirl in.
Bake for about 30 - 35 minutes, or until a toothpick comes out clean. Allow to cool completely, then remove from the pan and slice.
Notes
*The nutmeg is only needed depending on the brand of eggnog you use. I actually found that the eggnog I used could use a bit more nutmeg after being reduced and added to the cheesecake batter.