Preheat the oven to 350°F.
In a large bowl, mix cream cheese, brown sugar, granulated sugar, and cornstarch until smooth.
Add mashed bananas, brown butter, sour cream, cinnamon, vanilla extract, and rum extract, and mix until combined.
Add eggs and egg yolks one at a time, mixing until fully incorporated.
Pour 1/3 of the cheesecake batter into the crust, sprinkle with 1/3 of the cinnamon filling, and repeat layers twice. Swirl gently with a knife.
Place the springform pan in a larger roasting pan and pour hot water into the roasting pan until it reaches about 1 ½ inches up the sides of the springform pan.
Bake for 1 hour, then leave in the oven with the door cracked open for another hour to cool.
Once cooled, refrigerate for at least 8 hours or overnight.