Preheat the oven to 325°F (163°C). Boil a kettle of water for the water bath. Lightly grease a 9-inch springform pan and wrap the outside with a double layer of foil, securing it tightly to prevent water from getting in.
In a bowl, mix together the graham cracker crumbs, melted butter, and ¼ cup sugar until well combined. Press the mixture into the bottom of the prepared springform pan to form the crust. Bake in the preheated oven for 10 minutes, then remove and set aside.
In a large mixing bowl, beat the cream cheese and 1 cup sugar until smooth and creamy. Add the eggs, one at a time, beating well after each addition.Mix in the flour, ensuring there are no lumps. Add the eggnog, vanilla extract, ground nutmeg, and salt, and continue to beat until everything is well combined and smooth.
Place the prepared pan in a larger baking dish or roasting pan. Pour the boiling water into the larger dish until halfway up the sides of the springform pan.
Pour the filling over the prepared crust. Transfer to the oven and bake in the preheated oven for 60 minutes or until the center is set and the top is lightly browned. Turn off the oven and leave the cheesecake in the oven for an additional hour.
After an hour, carefully remove the cheesecake from the water bath and place it on a wire rack to cool to room temperature. Once cooled, refrigerate the cheesecake for at least 4 hours, or overnight for best results.
Before serving, optionally top the cheesecake with whipped cream and a sprinkle of ground cinnamon and nutmeg. Release the cheesecake from the springform pan and transfer it to a serving plate. Slice and serve chilled.