Preheat the oven to 350°F.
Add the brown sugar to a large bowl.
Add your butter to a skillet on medium heat. Stir until it is melted. Continue to stir as it begins to foam slightly. When you see light brown flecks begin to appear at the bottom of the butter, continue stirring and keep an eye on it. Things will happen fast at this point. When the flecks turn golden brown remove the butter from the heat and continue to stir.
When the flecks are a deep brown, pour the butter into the bowl with the brown sugar. Immediately whisk to combine.
Let this mixture cool for 5-10 minutes while you mash the bananas.
Once it is cool, whisk in the eggs and vanilla first, then add the bananas. Stir well.
Directly add the flour, baking soda and salt. Stir with a spatula to combine.
Split the batter into two bowls now. Use a small blender or food processor to blend the sesame seeds into a sand-like texture and add them to one half of the batter and mix.
In a parchment-lined loaf pan, add about 1/4 of the banana batter to the bottom and spread it out thinly. Then add a layer of the black sesame batter and spread it out. Repeat this process until all the batter is used up.
Insert a long skewer into the bread and swirl to create a marble pattern (optional, but fun!)
Bake at 350°F for 50-60 minutes or until the loaf is a deep golden brown.
Let cool, then slice and serve!