Preheat oven to 350 degrees F. Lightly grease the bottom and sides of a 9x13 baking dish.

In a medium mixing bowl, mix together the graham cracker crumbs and melted butter until evenly moistened.

Press crumb mixture into the bottom and about 1/2-inch up the sides of the pan.

In a medium mixing bowl, whisk together the flour, sour cream, and vanilla extract Set aside.

In a stand mixer with the paddle attachment, beat together the cream cheese, goat cheese, mascarpone and sugar until evenly incorporated, 3 to 5 minutes.

Pour the eggnog and rum into cream cheese mixture and mix until just combined.

Whisk in eggs, one at a time, scraping down the sides of the bowl after each addition.

Stir in the sour cream mixture and mix until combined.

Pour the mixture into prepared pan and bake in the preheated oven until the edges have nicely puffed and the surface of the cheesecake is firm except for a small spot in the center that will jiggle when the pan is gently shaken, about 30 minutes.

When the cheesecake is done, turn off the oven and let it cool in the oven for 3 to 4 hours. This prevents any cracks from forming on the top of the cheesecake.

Remove from the oven and let cheesecake cool completely before covering and storing in the fridge between 4 to 8 hours, preferably overnight.