Preheat the oven to 325°F. Line the bottom of a high-sided 9-inch springform pan with parchment paper. Using a strip, line the sides as well. Use a small dab of vegetable shortening to get it to stick. Wrap the bottom of the springform pan tightly with aluminum foil to prevent leaking. make sure the foil reaches about 3/4 way up the sides to prevent the water bath from seeping inside. Set aside.
Find a high sided roasting pan that the springform pan fits inside. It does not need to be higher sided than the springform pan. Using a water bath is optional, but will prevent cracks in the cake and also has been shown to make for a creamy filling. If you choose not to use a water bath, place the pan onto a dry rimmed baking sheet. Set aside until ready to bake.
Crust:
In a medium mixing bowl, stir together the graham cracker crumbs, melted butter, sugar, cinnamon and nutmeg until it resembles wet sand.
Pour this into the bottom of the springform pan and press down using the bottom of a measuring cup to form a bottom crust only.
Bake for 10 minutes (just the pan, NOT the water bath) and remove.
Cheesecake Filling:
In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl using an electric hand mixer, beat the cream cheese until soft and smooth. Add the sugar, flour, cinnamon and nutmeg, blending until just combined.
Add the eggnog, vanilla extract and rum extract until smooth. Mixture may start sloppy, but will blend together.
Add the eggs, one at a time, until incorporated, trying not to overmix.
Pour the cheesecake batter over the pie crust. Place the pan into the roasting pan then using a measuring cup, pour hot tap water around it until it reaches about half way up the side, but not above the aluminum foil. Bake the cheesecake for approximately 1 hour and 10 minutes, turning 180° halfway through baking to cook evenly. If the top starts to brown, gently lay a piece of aluminum foil over top (doesn't need to be fitted on, just loosely). The cake should be set and not jiggle in the center.
Turn the oven off and crack the oven door about an inch (however small your oven will crack without shutting or opening wide). If you placed aluminum foil over top, remove it now.
Allow the cheesecake to cool in the oven until it is room temperature.
Remove it (and the water bath) from the oven and the cake pan from the water bath. Take off the aluminum foil bottom. Cover the cake and chill in the refrigerator for a minimum of 4 hours, but better overnight.
When ready to serve or display, unhinge the spring form pan and gently peel away the parchment strips from the side. You can try to release the bottom parchment, but honestly I transfer mine to a serving platter or plate with the parchment still on or leave it on the bottom of the springform pan and decorate around the bottom to cover the seam.
Top each slice or the whole cake with whipped cream and sugared cranberries.