Add sugar and water to a pot over medium heat. Cook until it turns deep amber, slightly past golden. Immediately pour into the cake pan and swirl to evenly coat the bottom.

Mash bananas until smooth. Whisk together bananas, sugar, brown butter, eggs, and vanilla until fully combined.

Add flour, cocoa powder, baking powder, salt, milk, and espresso powder. Mix just until smooth and fully incorporated. Do not overmix.

In a separate bowl, combine sweetened condensed milk, evaporated milk, and eggs. Blend until completely smooth with no separation.

Pour the cake batter into the caramel-lined pan, filling about 40 to 45 percent of the pan.

Slowly pour the flan mixture directly into the center of the cake batter, filling about 30 percent of the pan.

Cover the pan tightly with foil. Place it inside a larger pan with a rack underneath. Add warm water (about 150°F) to the outer pan until it reaches the level of the custard.

Bake at 350°F for 60 minutes, checking at 45 minutes. The cake is done when a toothpick inserted into the cake layer comes out clean and the center jiggles slightly.

Cool at room temperature for 2 hours, then refrigerate overnight until fully set.

To release, warm the bottom of the pan with hot water or a torch, then flip onto a serving plate.