Preheat the oven to 325 degrees F (165 degrees C).

Mix graham cracker crumbs, melted butter, and sugar together in a medium bowl until well combined.

Press graham mixture into the bottom of a 9-inch springform pan.

Bake in the preheated oven for 10 minutes; transfer the pan to a wire rack and allow crust to cool.

Increase the oven temperature to 425 degrees F (220 degrees C).

While the crust is cooling, combine cream cheese, sugar, eggnog, and flour in a food processor; process until smooth.

Blend in eggs, rum, and nutmeg.

Pour eggnog mixture into cooled crust.

Bake in the preheated oven for 10 minutes.

Reduce the heat to 250 degrees F (120 degrees C) and continue to bake until edges are puffed and surface is firm except for a small spot in the center that will jiggle when the pan is gently shaken, about 45 minutes.

Loosen the sides of the springform pan; let cheesecake cool before removing the rim completely.