Preheat the oven to 350F (180C) degrees and position the oven rack on the bottom ⅓ of the oven.
Wrap the outside of a 9-inch springform pan in aluminum foil at least 3 times so that all the seems are covered and no areas are showing.
In a medium-sized bowl, stir together the gingersnap crumbs and brown sugar. Stir in the melted butter
Press the mixture into the bottom of the prepared pan.
Bake in the preheated oven for 8 minutes. Then remove from the oven, leaving the oven turned on.
In a very large bowl, beat the cream cheese until soft. Turn down the mixer and scrape down the sides of the bowl as necessary.
Beat in the sugar, cornstarch and nutmeg.
With the mixer on low speed, mix in the vanilla extract, rum/rum extract, and eggnog.
Beat in the eggs, mixing only until just combined.
Place the cheesecake crust in the middle of a large roasting pan, then pour the cheesecake filling on top of the crust.
Pour the hot water into the roasting pan, so that there's about ½-1 inch of water in the bottom of the roasting pan.
Place the roasting pan with the cheesecake inside in the oven and bake for 50-60 minutes, or until the top looks almost set, except for in the very middle.
Remove from the oven. Cool the cheesecake in the water bath until room temperature.
Then remove the springform pan from the roasting pan, cover the cheesecake, and refrigerate for at least 6 hours.
When ready to serve, trace around the edges of the cheesecake with a very thin knife. Then unclamp the springform pan.
Optionally, sprinkle with a little extra nutmeg and dollop each slice with whipped cream.
Store leftovers covered in the fridge for up to 3 days. Cheesecake is best if enjoyed the day after it's baked. Cheesecake can be wrapped tightly and frozen for up to 3 months, then thaw in the fridge before enjoying.