Preheat the oven to 350 F. Line the bottom of a 9” springform pan with parchment paper and lightly spray the sides of the pan with baking spray.
In a medium sized bowl, combine the gingersnap crumbs and brown sugar. Add in the butter and mix until the mixture resembles wet sand. Press into an even layer in the bottom of the prepared springform pan. Place into the preheated oven to bake for 15 minutes. Once baked, remove from the oven and place onto a cooling rack.
While the crust bakes, make the cheesecake batter. Add the cream cheese and sugar to the bowl of a stand mixer fitted with a paddle attachment. Beat on medium high speed for 1 minute or until the mixture is smooth. Add in the whole eggs and beat for 30 seconds. Add in the egg yolks and beat for another 30 seconds. Next, add in the eggnog and yogurt. Beat for 30 seconds to incorporate. Lastly, add in the flour, cinnamon, rum extract and freshly grated nutmeg. Beat for 30 seconds.
Once the cheesecake batter is complete and smooth, pour into the baked crust. Wrap the bottom and sides of the springform pan with tinfoil to keep water from seeping in. Place into a larger pan. Fill the larger pan with enough water to come halfway up the sides of the springform pan to create a water bath. Place into the hot oven to bake for an hour and a half. Once baked, turn off the heat and leave the cheesecake in, undisturbed, for an additional hour. Keep the oven door closed.
Once the cheesecake has set for an hour, remove from the oven and unwrap the tinfoil. Place the cheesecake onto a cooling rack to cool completely. Once it is completely cooled, cover with tinfoil and place into the fridge to chill for at least 8 hours and up to overnight. Once chilled, carefully run a butter knife around the edge of the springform pan to release the cheesecake. Gently release the springform and remove the sides from the cheesecake. To remove the cheesecake from the springform pan base, carefully slide a butter knife underneath the crust and run it around all of the sides to release it from the base. Carefully slide it off onto a cake stand or serving platter. It is now ready to serve. Keep the cheesecake chilled until ready to serve.
Storage: Cheesecake may be stored in an airtight container in the fridge for up to 1 week or in the freezer for up to 3 months.