Preheat the oven to 325°F (163°C).
Prepare the crust by mixing graham cracker crumbs and melted butter in a bowl until fully combined.
Press the crumb mixture into the bottom of a springform pan, packing it down firmly.
Bake the crust for 10 minutes, then remove and let cool.
In a large bowl, beat the cream cheese until creamy and smooth, about 2-3 minutes.
Gradually add sugar and continue to beat until well combined and fluffy.
Add the eggs one at a time, mixing well after each addition.
Next, blend in eggnog, vanilla extract, nutmeg, and cinnamon until smooth.
Pour the filling over the cooled crust and smooth the top.
Bake for 50-60 minutes, until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside for 1 hour to cool gradually.
Remove from the oven and let cool completely before refrigerating for at least 4 hours or overnight.
Serve topped with whipped cream and a sprinkle of nutmeg or cinnamon.