Preheat the oven to 350 degrees if it's not still preheated from the crust.
In a large bowl of a stand mixer, mix the cream cheese, brown sugar, granulated white sugar and cornstarch together with a paddle attachment on medium speed for two minutes until everything is smooth and there are no lumps. (You can alternatively use a hand mixer.) Scrape down the bottom and sides of the bowl to ensure everything has been mixed well.
32 oz (907 g) cream cheese, softened, 3/4 cup (165 g) brown sugar, packed, 1/4 cup (50 g) granulated white sugar, 2 tbsp (16 g) cornstarch
Add the mashed bananas, brown butter, sour cream, cinnamon, vanilla and rum extract to the cream cheese mixture and mix for 1 minute on medium speed. Scrape the sides and bottom of bowl again to ensure everything is mixed together.
1 cup (250 g) very ripe bananas, mashed, 1/3 cup (82 g) sour cream, at room temperature, 1 tbsp cinnamon, 1 tbsp vanilla extract, 2 tsp rum extract
At this point, stop and put a pot of water on the stove to start boiling for the water bath. You will want enough water to go up about 1 ½ inches on the sides of the springform pan.
Next add in the eggs and egg yolks one at a time to the cheesecake batter. Mix on medium speed, ensuring that each is fully mixed in before adding the next. As soon as the last one is fully mixed in, turn off the mixer. Do not over mix the batter.
3 whole eggs, at room temperature, 2 egg yolks, at room temperature
Pour 1/3 of the cheesecake batter into the prepared crust. Sprinkle 1/3 of the cinnamon filling over the cheesecake batter. Pour 1/3 of the cheesecake batter over this layer and top with 1/3 of the cinnamon filling. Repeat the step once more, then gently swirl the cinnamon filling and cheesecake batter with a butter knife.
Place the cheesecake in a large roasting pan. Transfer to the oven and pour the hot water into the pan being very careful not to splash the cheesecake.
Bake the cheesecake at 350 degrees for 1 hour. When 1 hour is up, turn off the oven and crack the oven door open using a wooden utensil. Let the cheesecake stay in the oven for 1 more hour. The cheesecake will continue to bake as it is cooling.
Remove cheesecake from oven and go around the edges of the pan with a butter knife to loosen the crust from the sides of the pan. Let it cool completely on a wire rack. Cover with plastic wrap or aluminum foil, then chill the cheesecake in the fridge for 8 hours, or overnight.