Preheat the oven to 350°F (175°C).
Prepare the crust by mixing graham cracker crumbs, melted butter, and sugar in a medium bowl until well combined.
Press the crust mixture into the bottom of a 9-inch springform pan in an even layer. Bake for 10 minutes, then set aside to cool.
In a large mixing bowl, beat softened cream cheese on medium speed until smooth and creamy, about 2-3 minutes.
Gradually add 1 cup of granulated sugar to the cream cheese while continuing to beat until well combined.
Mix in the eggnog, eggs, vanilla extract, nutmeg, and cinnamon until just combined, taking care not to overmix.
Pour the filling over the cooled crust, smoothing the top with a spatula.
Bake the cheesecake in the preheated oven for 50-60 minutes, or until the edges are set but the center is still slightly jiggly.
Turn off the oven and crack the door, letting the cheesecake cool inside for 1 hour.
Remove from the oven, let cool to room temperature, then refrigerate for at least 4 hours, preferably overnight, before serving.