Preheat your oven to 325 degrees F. Grease a 9-inch springform pan to ensure easy removal of your cheesecake later on.
To make the cranberry mixture, combine granulated sugar and cornstarch in a medium saucepan. Whisk in the cranberry juice until smooth. Next, stir in the fresh or frozen cranberries and place the pan over medium heat. Bring the mixture to a rolling boil and cook for about 2 minutes, stirring continuously until it thickens. Once thickened, remove from heat and set aside.
For the crust, in a medium bowl, combine graham cracker crumbs and sugar. Drizzle the melted butter over the crumbs and mix until well combined. Transfer the crumb mixture to the prepared pan and press it down firmly to create an even layer. Place the pan on a rimmed baking sheet and bake for 10 minutes. Allow it to cool on a wire rack.
While the crust cools, prepare the cheesecake filling. In a large mixing bowl, use an electric mixer on medium-high speed to beat the cream cheese and granulated sugar until the mixture is smooth and fluffy, about 3 minutes. Then, add the all-purpose flour and mix until just combined.
Next, reduce the mixer speed to low and add the eggs one at a time, ensuring each is fully incorporated before adding the next. Don't forget to scrape down the sides of the bowl as needed. Finally, add the eggnog and vanilla extract, mixing until everything is just combined.
Pour two-thirds of the cheesecake batter into the prepared pan over the cooled crust. Spoon half of the cranberry mixture on top of the batter, covering it evenly. Then, slowly pour the remaining cheesecake batter over the cranberry layer.
Return the springform pan to the rimmed baking sheet and bake for about 1 hour and 15 minutes. The edges should be set, but the center will still jiggle slightly.
Once baked, carefully remove the pan and let it cool on a wire rack for 10 minutes. Run a knife around the edge of the pan to loosen the cheesecake, then cool for an additional hour. Afterward, place the cheesecake in the refrigerator and chill overnight, allowing it to firm up completely.
When you're ready to serve, remove the sides of the springform pan and top the cheesecake with the remaining cranberry mixture. Enjoy this festive delight!
