Preheat your oven to 350°F (175°C). Lightly grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and 1/2 tsp ground nutmeg. Pour in melted unsalted butter and mix until crumbs are moistened. Press mixture firmly and evenly into the bottom of the prepared springform pan.
Place the pan in the preheated oven and bake for 8-10 minutes until lightly golden. Remove from oven and let cool completely.
In a large bowl, beat softened cream cheese with 1 cup granulated sugar using an electric mixer until smooth and creamy.
Beat in 3 tbsp all-purpose flour until just combined. Add eggnog, 2 tbsp rum extract (or vanilla extract), 1/2 tsp ground nutmeg, and 1/4 tsp ground cinnamon. Beat on low speed until incorporated.
Add 3 large eggs one at a time, beating on low speed after each addition until just combined. Do not overmix.
Pour filling over cooled crust and smooth the top.
Bake at 350°F (175°C) for 55-65 minutes, until edges are set and the center has a slight jiggle.
Turn off the oven, crack the door open slightly, and leave cheesecake inside for 1 hour to cool gradually.
Remove from oven and let cool completely on a wire rack. Cover loosely and chill in the refrigerator for at least 4 hours, or preferably overnight.
Just before serving, whip heavy cream with powdered sugar and rum extract until soft peaks form.
Carefully release the sides of the springform pan. Top with whipped cream, slice, and serve.