For the Brown Butter:

1. Heat the butter in a pot over medium heat until it turns brown and nutty. This should take about 5 minutes. Remove from heat and transfer to a bowl.

For the Brown Sugar Cinnamon Filling:

1. Combine softened butter, brown sugar, cinnamon, and flour in a bowl and mix until smooth. Set aside.

For the Crust:

1. Preheat the oven to 350°F.
2. Prepare a 9-inch springform pan by wrapping the bottom and edges with aluminum foil and lining the bottom with parchment paper.
3. Crush the graham crackers in a food processor, then mix in melted butter and brown sugar until combined.
4. Press the mixture into the bottom and up the sides of the pan and bake for 10 minutes. Let it cool.

For the Banana Cheesecake:

1. Preheat the oven to 350°F.
2. In a large bowl, mix cream cheese, brown sugar, granulated sugar, and cornstarch until smooth.
3. Add mashed bananas, brown butter, sour cream, cinnamon, vanilla extract, and rum extract, and mix until combined.
4. Add eggs and egg yolks one at a time, mixing until fully incorporated.
5. 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.
6. 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.
7. Bake for 1 hour, then leave in the oven with the door cracked open for another hour to cool.
8. Once cooled, refrigerate for at least 8 hours or overnight.

For the Bananas Foster Topping:

1. In a saucepan, melt butter and brown sugar over medium heat, then simmer for 5 minutes.
2. Reduce heat, add cream, rum extract, vanilla extract, and salt, and simmer for 1-2 minutes.
3. Add banana slices and simmer for 6-8 minutes until slightly transparent. Remove from heat and let cool.

For the Cream Cheese Frosting:

1. Beat butter until pale and fluffy, then add cream cheese and mix until smooth. Gradually add powdered sugar until light and fluffy.

Assembling the Cheesecake:

1. Transfer cheesecake to a serving plate, pipe frosting around the edges, and pour bananas foster topping over the center. Then serve and enjoy!