Prepare the Crust: Preheat your oven to 325°F (160°C). In a mixing bowl, combine the graham cracker crumbs and melted butter. Stir until the crumbs are fully coated and resemble wet sand. Press the mixture evenly into the bottom of a 9-inch springform pan. Use the back of a spoon or the bottom of a glass to compact it firmly.Bake the crust for 8-10 minutes. Remove and set aside to cool slightly.
Make the Filling: In a large mixing bowl, beat the softened cream cheese until smooth and creamy (about 2 minutes). Gradually add the sugar, mixing until fully incorporated. Scrape down the sides of the bowl as needed. Beat in the eggs, one at a time, ensuring each egg is well-mixed before adding the next. Slowly pour in the eggnog, vanilla extract, nutmeg, and salt. Mix on low speed until the batter is smooth and evenly combined.
Assemble and Bake: Pour the cheesecake filling over the prepared crust, spreading it evenly with a spatula. Place the springform pan in a larger baking pan and pour about 1 inch of hot water into the outer pan to create a water bath (this helps prevent cracks). Carefully transfer to the oven and bake for 50-55 minutes. The edges should be set, but the center will have a slight jiggle.
Cool the Cheesecake: Turn off the oven and crack the door slightly, allowing the cheesecake to cool gradually for 1 hour. Remove from the oven, then run a knife gently around the edges to prevent sticking. Let it cool to room temperature. Cover the cheesecake and chill in the refrigerator for at least 4 hours or overnight for best results.
Serve and Garnish: Before serving, garnish with a dollop of whipped cream, a sprinkle of freshly grated nutmeg, and optional cinnamon sticks for a festive touch.